UNIVERSIDADE NOVA DE LISBOA FACULDADE DE CIÊNCIAS E TECNOLOGIA DEPARTAMENTO DE MATEMÁTICA UMA ABORDAGEM COMPARATIVA E ANALÍTICA DE DOIS SISTEMAS DE BONUS

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❯◆■❱❊❘❙■❉❆❉❊ ◆❖❱❆ ❉❊ ▲■❙❇❖❆

❋❆❈❯▲❉❆❉❊ ❉❊ ❈■✃◆❈■❆❙ ❊ ❚❊❈◆❖▲❖●■❆

❉❊P❆❘❚❆▼❊◆❚❖ ❉❊ ▼❆❚❊▼➪❚■❈❆

  

❯▼❆ ❆❇❖❘❉❆●❊▼ ❈❖▼P❆❘❆❚■❱❆ ❊

❆◆❆▲❮❚■❈❆ ❉❊ ❉❖■❙ ❙■❙❚❊▼❆❙ ❉❊ ❇❖◆❯❙

▼❆▲❯❙ ❊▼ ❈❆❇❖ ❱❊❘❉❊✿

❖ ❙■❙❚❊▼❆ ❆❈❚❯❆▲ ❊ ❆ P❘❖P❖❙❚❆ ❉❆

  

●❆❘❆◆❚■❆

▲✐❝❡♥❝✐❛❞❛ ❊✉r✐s❛♥❞❛ ❱❡♥✉❧❞❛ ❈❛r❞♦s♦ ❚❛✈❛r❡s ❘♦❞r✐❣✉❡s

❖r✐❡♥t❛❞♦r❛✿ Pr♦❢❡ss♦r❛ ❉♦✉t♦r❛ ●r❛❝✐♥❞❛ ●✉❡rr❡✐r♦

  

❈♦✲❖r✐❡♥t❛❞♦r❛✿ Pr♦❢❡ss♦r❛ ❉♦✉t♦r❛ ▲♦✉r❞❡s ❆❢♦♥s♦

▼❡str❛❞♦ ❡♠ ▼❛t❡♠át✐❝❛ ❡ ❆♣❧✐❝❛çõ❡s

✭❆❝t✉❛r✐❛❞♦✱ ❊st❛tíst✐❝❛ ❡ ■♥✈❡st✐❣❛çã♦ ❖♣❡r❛❝✐♦♥❛❧✮

  

❏❛♥❡✐r♦ ✷✵✶✶

  ✵

  ❆❣r❛❞❡❝✐♠❡♥t♦s

  ➚s ♠✐♥❤❛s ♦r✐❡♥t❛❞♦r❛s✱ ❛ Pr♦❢❡ss♦r❛ ●r❛❝✐♥❞❛ ●✉❡rr❡✐r♦ ❡ ❛ Pr♦❢❡ss♦r❛ ▲♦✉r❞❡s ❆❢♦♥s♦✱ ♣❡❧❛ ❞❡❞✐❝❛çã♦✱ ❛❥✉❞❛ ❡ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ q✉❡ ❞❡♠♦♥str❛r❛♠ ❛♦ ❧♦♥❣♦ ❞❡st❡ tr❛❜❛❧❤♦✳

  ➚ ❙❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ q✉❡ ❞✐s♣♦♥✐❜✐❧✐③♦✉ ♦s ❞❛❞♦s✱ s❡♠ ♦s q✉❛✐s ♥ã♦ s❡r✐❛ ♣♦ssí✈❡❧ ❡❢❡❝t✉❛r ❡st❡ tr❛❜❛❧❤♦✳

  ❆♦s ♠❡✉s ❝♦❧❡❣❛s ❡ ❛♠✐❣♦s✱ ♣❡❧♦ ❛♣♦✐♦✱ ✐♥❝❡♥t✐✈♦ ❡ ❛♠✐③❛❞❡ ❞❛❞❛ ❛♦ ❧♦♥❣♦ ❞❡ t♦❞♦s ❡st❡s ❛♥♦s ❞❡ ❢❛❝✉❧❞❛❞❡✳

  ➚ ♠✐♥❤❛ ❢❛♠í❧✐❛✱ ❡♠ ❡s♣❡❝✐❛❧ à ♠✐♥❤❛ ✐r♠ã✱ ♣❡❧♦ ❛♣♦✐♦ ✐♥❝♦♥❞✐❝✐♦♥❛❧ q✉❡ s❡♠♣r❡ ❞❡♠♦♥str♦✉✳

  P♦r ú❧t✐♠♦✱ ✉♠ ❛❣r❛❞❡❝✐♠❡♥t♦ ♠✉✐t♦ ❡s♣❡❝✐❛❧ ❛♦s ♠❡✉s ♣❛✐s✱ q✉❡ ♠❡s♠♦ ❡st❛♥❞♦ ❧♦♥❣❡✱ ❡st✐✈❡r❛♠ s❡♠♣r❡ ♣r❡s❡♥t❡s✳

  ❈♦♣②r✐❣❤t

  ❘❡s✉♠♦

  ◆❡st❛ ❞✐ss❡rt❛çã♦ ♣r❡t❡♥❞❡✲s❡ ❛✈❛❧✐❛r ♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❞❡ ✉♠❛ ❙❡❣✉r❛❞♦r❛ ❝❛❜♦✲✈❡r❞✐❛♥❛✱ s♦❜ ❛ ♣❡rs♣❡❝t✐✈❛ ❞❡ ✉♠❛ ❝❛rt❡✐r❛ ❛❜❡rt❛✱ r❡❝♦rr❡♥❞♦ ❛♦ ▼♦❞❡❧♦ ❞♦s ❱órt✐❝❡s ❊st♦❝ást✐❝♦s ✐st♦ é✱ ❛❞♠✐t✐♥❞♦ q✉❡ ❤á ❡♥tr❛❞❛s ❡ s❛í❞❛s ❞♦s s❡❣✉r❛❞♦s ❞❛ ❝❛rt❡✐r❛ ❞❛ s❡❣✉r❛❞♦r❛✳ ◆❛ ❛♣❧✐❝❛çã♦ ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ❝❛❜♦✲✈❡r❞✐❛♥❛ ●❛r❛♥t✐❛✳ P❛r❛ ❡❢❡✐t♦s ❝♦♠♣❛r❛t✐✈♦s ❛✈❛❧✐♦✉✲s❡ t❛♠❜é♠ ♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s r❡❝♦rr❡♥❞♦ ❛♦ ♠♦❞❡❧♦ ❝❧áss✐❝♦✳ ❊st✐♠♦✉✲s❡✱ s♦❜ ❛♠❜❛s ❛s ♣❡rs♣❡❝t✐✈❛s✱ ❛s ❞✐str✐❜✉✐çõ❡s ❧✐♠✐t❡ ❛ss♦❝✐❛❞❛s ❛♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❞❛ ❙❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛✱ ❙✳❆✳✱ ❜❡♠ ❝♦♠♦ ❛s ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s ♣r♦♣♦st❛s ♣♦r ❛❧❣✉♥s ❛✉t♦r❡s ●✐❧❞❡ ✫ ❆✈❛❧✐♦✉✲s❡ ♦ s✐st❡♠❛ ✉t✐❧✐③❛♥❞♦ ❛s ♠❡❞✐❞❛s ❞❡ r❡❝♦rr❡♥❞♦ às ❡s❝❛❧❛s ó♣t✐♠❛s ♦❜t✐❞❛s✳ ❉❛❞♦ q✉❡ ♦ s✐st❡♠❛ ❛❝t✉❛❧ ✉t✐❧✐③❛❞♦ ♥❛ ❙❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛✱ ❙✳❆✳ ❛♣r❡s❡♥t❛ ❛❧❣✉♠❛s ✐♥❝♦❡rê♥❝✐❛s ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞❛ ❡✜❝á❝✐❛ ❞❛ t❛r✐❢❛çã♦ ❛ ♣♦st❡r✐♦r✐✱ ❛♥❛❧✐s♦✉✲s❡ ❡ ❛✈❛❧✐♦✉✲s❡ ✉♠ ♥♦✈♦ s✐st❡♠❛ ♣r♦♣♦st♦ ♣♦r ❝♦♥❢♦r♠❡ s✉❣❡stã♦ ❞❛ ❙❡❣✉r❛❞♦r❛✳ ❈♦♠ ❜❛s❡ ♥♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s✱ ❢♦✐ ❢❡✐t❛ ✉♠❛ ❛♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❡♥tr❡ ♦ s✐st❡♠❛ ❛❝t✉❛❧ ❡ ♦ s✐st❡♠❛ ♣r♦♣♦st♦ ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛✳ P❛❧❛✈r❛s ❈❤❛✈❡✿❇♦♥✉s ▼❛❧✉s✱ ▼♦❞❡❧♦ ❈❧áss✐❝♦✱ ❱órt✐❝❡s ❊st♦❝ást✐❝♦s✱ ❉✐str✐❜✉✐çã♦ ▲✐♠✐t❡✱ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s✱ ▼❡❞✐❞❛s ❞❡ ❆✈❛❧✐❛çã♦✳

  ❆❜str❛❝t

  ❚❤❡ ♣✉r♣♦s❡ ♦❢ t❤✐s t❤❡s✐s ✐s t♦ ❡✈❛❧✉❛t❡ ❛ ❜♦♥✉s ♠❛❧✉s s②st❡♠ ♦❢ ❛ ❈❛♣❡ ❱❡r❞❡❛♥ ■♥s✉r❡r✱ ❢r♦♠ t❤❡ ♣❡rs♣❡❝t✐✈❡ ♦❢ ❛♥ ♦♣❡♥ ♣♦rt❢♦❧✐♦✱ ✉s✐♥❣ t❤❡ ❙t♦❝❤❛st✐❝ ❱♦rt✐❝❡s ♠♦❞❡❧ ✐✳❡✱ ❛ss✉♠✐♥❣ t❤❛t t❤❡r❡ ❛r❡ ❡♥tr✐❡s ❛♥❞ ❡①✐ts ♦❢ t❤❡ ♣♦rt❢♦❧✐♦✳ ■♥ t❤❡ ❛♣♣❧✐❝❛t✐♦♥ ✇❡ ✉s❡❞ ❞❛t❛ ❢r♦♠ t❤❡ ❈❛♣❡ ❱❡r❞❡❛♥ ✐♥s✉r❡r✱ ●❛r❛♥t✐❛✱ ❙✳❆✳✳ ❋♦r ❝♦♠♣❛r❛t✐✈❡ ♣✉r♣♦s❡s t❤❡ ❜♦♥✉s ♠❛❧✉s s②st❡♠ ✇❛s ❛❧s♦ ❡✈❛❧✉❛t❡❞ ✉s✐♥❣ t❤❡ ❝❧❛ss✐❝❛❧ ♠♦❞❡❧✳ ❋r♦♠ ❜♦t❤ ♣❡rs♣❡❝t✐✈❡s ✇❡ ❡st✐♠❛t❡ t❤❡ ❧✐♠✐t ❞✐str✐❜✉t✐♦♥s ♦❢ t❤❡ ❜♦♥✉s ♠❛❧✉s s②st❡♠ ♦❢ ●❛r❛♥t✐❛ ■♥s✉r❛♥❝❡ ❈♦♠♣❛♥②✱ ❛♥❞ t❤❡ ♦♣t✐♠❛❧ s❝❛❧❡s ♣r♦♣♦s❡❞ ❜② s♦♠❡ ❛✉t❤♦rs ❙✐♥❝❡ t❤❡ ❝✉rr❡♥t s②st❡♠ ✉s❡❞ ✐♥ t❤❡ ●❛r❛♥t✐❛✱ ❙✳❆✳ ✐♥s✉r❛♥❝❡ ❝♦♠♣❛♥②✱ ❤❛s s♦♠❡ ✐♥❝♦♥s✐st❡♥❝✐❡s ❢r♦♠ t❤❡ ❡✣❝✐❡♥❝② ♦❢ t❤❡ ❛ ♣♦st❡r✐♦r✐ ♣r❡♠✐✉♥s ♣♦✐♥t ♦❢ ✈✐❡✇✱ ❛ ♥❡✇ s②st❡♠ ♣r♦♣♦s❡❞ ❜② ✇❛s ❛♥❛❧②③❡❞ ❛♥❞ ❡✈❛❧✉❛t❡❞ ❛s s✉❣❣❡st❡❞ ❜② t❤❡ ✐♥s✉r❡r✳ ❇❛s❡❞ ♦♥ t❤❡s❡ r❡s✉❧ts ✇❡ ♣r❡s❡♥t ❛ ❝♦♠♣❛r❛t✐✈❡ ❛♥❛❧②s✐s ❜❡t✇❡❡♥ t❤❡ ❝✉rr❡♥t s②st❡♠ ❛♥❞ ●❛r❛♥t✐❛✬s ♣r♦♣♦s❡❞ s②st❡♠✳ ❑❡②✇♦r❞s✿❇♦♥✉s ▼❛❧✉s✱ ❈❧❛ss✐❝❛❧ ▼♦❞❡❧✱ ❙t♦❝❤❛st✐❝ ❱♦rt✐❝❡s✱ ▲✐♠✐t ❉✐str✐❜✉t✐♦♥s ✱ ❖♣t✐♠❛❧ ❙❝❛❧❡s ♦❢ ❛✇❛r❞s✱ ❊✈❛❧✉❛t❡ ▼❡❛s✉r❡s✳

  ❮♥❞✐❝❡

   ✐①

   ①✐

   ①✐✐✐

   ✶

   ✸

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵

   ✶✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹

   ✷✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺

  ✳ ✳ ✳ ✳ ✳ ✷✺ ✳ ✳ ✳ ✳ ✷✽

  ✈✐✐✐ ❮◆❉■❈❊

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷

  ✳ ✳ ✳ ✺✺

  

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

   ✼✺

   ✼✼

  ▲✐st❛ ❞❡ ❋✐❣✉r❛s

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✷

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✳ ✳ ✻✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✳ ✻✸ ✳ ✻✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻

  ▲✐st❛ ❞❡ ❚❛❜❡❧❛s

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✳ ✳ ✹✶ ✹✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✳ ✳ ✳ ✳ ✺✸ ✳ ✳ ✳ ✳ ✳ ✺✹

  ①✐✐ ▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙

  ✳ ✺✾ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✳ ✳ ✻✶

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✳ ✳ ✳ ✳ ✳ ✻✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✳ ✳ ✳ ✻✼ ✳ ✳ ✳ ✻✼ ✳ ✻✽ ✻✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸

  ■♥tr♦❞✉çã♦

  ❖s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s tê♠ ❝♦♠♦ ♦❜❥❡❝t✐✈♦ t❛r✐❢❛r ♦ ♣ré♠✐♦ ❞♦ s❡❣✉r❛❞♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ s✉❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✳ ❊st❡ ❝♦♥❝❡✐t♦ ❞❡ t❛r✐❢❛çã♦ é ❞❡♥♦♠✐♥❛❞♦ ♣♦r t❛r✐❢❛çã♦ ❛ ♣♦st❡r✐♦r✐ ✉♠❛ ✈❡③ q✉❡ ♦ ♣ré♠✐♦ ❛ ❛tr✐❜✉✐r ❛ ❝❛❞❛ s❡❣✉r❛❞♦ é ❞❡t❡r♠✐♥❛❞♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ s❡✉ ❤✐stór✐❝♦ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✱ ♦✉ s❡❥❛✱ ❛ s❡❣✉r❛❞♦r❛ ❝♦rr✐❣❡ ♦ ♣ré♠✐♦ ❛ ♣r✐♦r✐ ❞♦ s❡❣✉r❛❞♦ ❝♦♠ ❜❛s❡ ♥❛ s✉❛ ♣ró♣r✐❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✳

  ❊st❡ ❝♦♥❝❡✐t♦ ❞❡ t❛r✐❢❛çã♦ s✉r❣✐✉ ❡♠ ♠❡❛❞♦s ❞❛ ❞é❝❛❞❛ ❞❡ ✺✵✱ ❝♦♠ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ t♦r♥❛r ❛ t❛r✐❢❛çã♦ ❞♦ ♣ré♠✐♦ ♠❛✐s ❥✉st❛✱ ✈✐st♦ q✉❡ s❡♠ ✉♠❛ t❛r✐❢❛çã♦ ❛ ♣♦st❡r✐♦r✐✱ ♦s s❡❣✉r❛❞♦s ❞❡♥tr♦ ❞❡ ❝❛❞❛ ❝❧❛ss❡ ❞❡ r✐s❝♦ ❝♦♥t✐♥✉❛r✐❛♠✱ ♥♦ ❢✉t✉r♦✱ ❛ ♣❛❣❛r ♦ ♠❡s♠♦ ♣ré♠✐♦ ✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞♦s s✐♥✐str♦s ❞❡❝❧❛r❛❞♦s✱ ♦ q✉❡ s❡ tr❛❞✉③✐r✐❛ ❡♠ ♣ré♠✐♦s ❡q✉✐✈❛❧❡♥t❡s ♣❛r❛ r✐s❝♦s ♥ã♦ ❤♦♠♦❣é♥❡♦s✳ ❉❡st❛ ❢♦r♠❛✱ ❛tr❛✈és ❞❡ s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s é ♣♦ssí✈❡❧ t❛r✐❢❛r ♦s ♣ré♠✐♦s ❞♦s s❡❣✉r❛❞♦s ✐♥❞✐✈✐❞✉❛❧♠❡♥t❡✱ ❛❣r❛✈❛♥❞♦ ♦✉ ❜♦♥✐❢✲ ✐❝❛♥❞♦ ♦ ♣ré♠✐♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ s✉❛ s✐♥✐str❛❧✐❞❛❞❡ ❞❡❝❧❛r❛❞❛✳

  ❖s s❡❣✉r♦s ❞♦ r❛♠♦ ❛✉t♦♠ó✈❡❧ ❝♦♥st✐t✉❡♠✱ ♥❛ ❣❡♥❡r❛❧✐❞❛❞❡✱ ❛ ♠❛✐♦r ♣❛rt❡ ❞❛ ❝❛rt❡✐r❛ ❞♦s s❡❣✉r♦s ♥ã♦ ✈✐❞❛✳ ❉❛❞♦ q✉❡ ♦s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s ❝♦♥st✐t✉❡♠ ♦ ♣r✐♥❝✐♣❛❧ ♠ét♦❞♦ ❞❡ t❛r✐❢❛çã♦ ❛ ♣♦st❡r✐♦r✐ ♥❡st❡ t✐♣♦ ❞❡ s❡❣✉r♦✱ é ❡ss❡♥❝✐❛❧ ♣❛r❛ ❛s s❡❣✉r❛❞♦r❛s ♣♦ss✉ír❡♠ ✉♠ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ✭SBM✮ q✉❡ s❡❥❛ s✐♠✉❧t❛♥❡❛♠❡♥t❡ ❡✜❝❛③ ❡ ❝♦♠♣❡t✐t✐✈♦✳

  ❙❡♥❞♦ ✉♠ ❡❧❡♠❡♥t♦ ✐♠♣♦rt❛♥t❡ ♥❛ ❛❝t✐✈✐❞❛❞❡ s❡❣✉r❛❞♦r❛✱ ♦s SBM tê♠ ✈✐♥❞♦✱ ❛♦ ❧♦♥❣♦ ❞♦s t❡♠♣♦s✱ ❛ s✉s❝✐t❛r ✐♥t❡r❡ss❡ ❞❡ ♠✉✐t♦s ❛✉t♦r❡s ❡♠ ❡st✉❞❛r ❡ ❞❡s❡♥✈♦❧✈❡r ♠♦❞❡❧♦s q✉❡ s❡ ♣♦ss❛♠ ❛❞❡q✉❛r ❞❛ ♠❡❧❤♦r ❢♦r♠❛ ❛ ❡st❡ ❝♦♥❝❡✐t♦ ❞❡ t❛r✐❢❛çã♦✳

  ❆♦ ❧♦♥❣♦ ❞❡st❡ tr❛❜❛❧❤♦ s❡rã♦ ❞❡s❝r✐t♦s ❡ ❛♣❧✐❝❛❞♦s ❞♦✐s ♠♦❞❡❧♦s q✉❡ ❡①♣❧✐❝❛♠ ❡st❡ ❝♦♥❝❡✐t♦ ❞❡ t❛r✐❢❛çã♦✿ ♦ ♠♦❞❡❧♦ ❝❧áss✐❝♦✱ ❛q✉✐ ❞❡♥♦♠✐♥❛❞♦ ♣♦r ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ❡ ♦ ♠♦❞❡❧♦ ❞♦s ✈órt✐❝❡s ❡st♦❝ást✐❝♦s✱ ✈❡r ♣♦r ❡①❡♠♣❧♦✱ ❡ ❞❡♥♦♠✐♥❛❞♦ ❛q✉✐ ♣♦r ♠♦❞❡❧♦ ❛❜❡rt♦✳

  ◆♦ ✐♥í❝✐♦✱ ❡st❛ ❞✐ss❡rt❛çã♦ t✐♥❤❛ ❝♦♠♦ ♦❜❥❡❝t✐✈♦ ❛ ❛✈❛❧✐❛çã♦ ❞♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ✉s❛❞♦ ❡♠ ❈❛❜♦ ❱❡r❞❡✱ ✉s❛♥❞♦ ♣❛r❛ t❛❧ ♦s ❞❛❞♦s ❞❛ ❝♦♠♣❛♥❤✐❛ ❞❡ s❡❣✉r♦s ❝❛❜♦✲ ✈❡r❞✐❛♥❛ ●❛r❛♥t✐❛✱ ❙❆✳ ◆♦ ❡♥t❛♥t♦✱ ♥♦ ❞❡❝♦rr❡r ❞❛ ❛♥á❧✐s❡ ❞♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❛♣❧✐❝❛❞♦ ♥❡ss❡ ♣❛ís✱ ❢r✉t♦ ❞❛ ❧❡❣✐s❧❛çã♦ ❛❝t✉❛❧♠❡♥t❡ ❡♠ ✈✐❣♦r✱ ✈❡r✐✜❝♦✉✲s❡ q✉❡ ❡st❡ s✐st❡♠❛ ❛♣r❡s❡♥t❛ ❛❧❣✉♠❛s ❧❛❝✉♥❛s✱ ❛♣r❡s❡♥t❛♥❞♦✲s❡ ❝♦♠♦ ✉♠ s✐st❡♠❛ ❞❡s✐q✉✐❧✐❜r❛❞♦ t❛♥t♦ ♣❛r❛ ❛ s❡❣✉r❛❞♦r❛ ❝♦♠♦ ♣❛r❛ ♦ s❡❣✉r❛❞♦✳ ❊st❡ ❢❛❝t♦ ❥á t✐♥❤❛ s✐❞♦ ❛♥t❡s ✈❡r✐✜❝❛❞♦ ♣♦r q✉❡✱ ♣❛r❛ ❛❧é♠ ❞❡ ❝r✐t✐❝❛r ♦ ❛❝t✉❛❧ SBM ❛♣❧✐❝❛❞♦ ❡♠ ❈❛❜♦ ❱❡r❞❡✱ ♣r♦♣õ❡ ✉♠ SBM ❛❧t❡r♥❛t✐✈♦ q✉❡ ♣♦❞❡rá s❡r ❢✉t✉r❛♠❡♥t❡ ✉t✐❧✐③❛❞♦✳ ❈♦♥s✐❞❡r♦✉✲s❡ ❡♥tã♦ q✉❡ s❡r✐❛ ♠❛✐s ✐♥t❡r❡ss❛♥t❡✱ ♣❛r❛ ❛❧é♠ ❞❡ ❛✈❛❧✐❛r ♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s q✉❡

  ✷ ▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙

  ❢✉t✉r❛♠❡♥t❡✱ ❡❢❡❝t✉❛♥❞♦✱ ♣♦st❡r✐♦r♠❡♥t❡✱ ❝♦♠♣❛r❛çõ❡s ❡♥tr❡ ❡st❡s ❞♦✐s s✐st❡♠❛s✳ ❖ tr❛❜❛❧❤♦ ❡stá ❡str✉t✉r❛❞♦ ❡♠ ✸ ❝❛♣ít✉❧♦s✳ ◆♦ ♣r✐♠❡✐r♦ ❝❛♣ít✉❧♦ é ❢❡✐t❛ ✉♠❛ ❜r❡✈❡ ✐♥tr♦❞✉çã♦ ❛♦s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s

  ✭SBM✮ ❡♠ ❣❡r❛❧✱ ❜❡♠ ❝♦♠♦ ✉♠❛ ❞❡s❝r✐çã♦ t❡ór✐❝❛ ❞♦s ♠♦❞❡❧♦s ❢❡❝❤❛❞♦ ❡ ❛❜❡rt♦✱ ✈❡r ♣♦r ❡①❡♠♣❧♦✱

  ❖ s❡❣✉♥❞♦ ❝❛♣ít✉❧♦ é ❞✐✈✐❞✐❞♦ ❡♠ ❞✉❛s s❡❝çõ❡s✳ ◆❛ ♣r✐♠❡✐r❛ s❡❝çã♦ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ❡s❝❛❧❛s ó♣t✐♠❛s ❞❡ ♣ré♠✐♦s ❞❡t❡r♠✐♥❛❞❛s ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ❞❡ ♠♦❞❡❧♦ ❞❡ ❡ ❞♦ ♠♦❞❡❧♦ ❞❡ ◆❛ s❡❣✉♥❞❛ s❡❝çã♦ sã♦ ❞❡s❝r✐t❛s ❛s ♠❡❞✐❞❛s ❞❡ ❛✈❛❧✐❛çã♦ ❛♣r❡s❡♥t❛❞❛s ♣♦r

  ❖ t❡r❝❡✐r♦ ❝❛♣ít✉❧♦✱ ♦ ♣r✐♥❝✐♣❛❧ ❞❡st❡ tr❛❜❛❧❤♦✱ ❝♦♥s✐st❡ ♥❛ ❛♣❧✐❝❛çã♦ ❞♦s ♠♦❞❡❧♦s ❛♣r❡s❡♥t❛❞♦s ♥♦s ❝❛♣ít✉❧♦s ❛♥t❡r✐♦r❡s à ❝❛rt❡✐r❛ ❞❛ ●❛r❛♥t✐❛✳ P❛r❛ ❛❧é♠ ❞❛ ❛♣❧✐❝❛çã♦ ❞❡ss❡s ♠♦❞❡❧♦s é ❢❡✐t❛ ✉♠❛ ❛♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ q✉❡r ❛♦ ♥í✈❡❧ ❞♦s ❞♦✐s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s q✉❡ ❛♦ ♥í✈❡❧ ❞❛ ♣❡rs♣❡❝t✐✈❛ ❞❡ ❝❛rt❡✐r❛ ❛❜❡rt❛ ❡ ❢❡❝❤❛❞❛✳ ❊st❡ ❝❛♣ít✉❧♦ ❡♥❝♦♥tr❛✲s❡ ❞✐✈✐❞✐❞♦ ❡♠ q✉❛tr♦ s❡❝çõ❡s✳

  ❆ ♣r✐♠❡✐r❛ s❡❝çã♦ ❝♦♥s✐st❡ ♥❛ ❛♣r❡s❡♥t❛çã♦ ❡ ❛♣❧✐❝❛çã♦ ❞❡ ❛❧❣✉♥s ♠♦❞❡❧♦s q✉❡ s❡ ♣♦ss❛♠ ❛❥✉st❛r ❛♦ ❢❡♥ó♠❡♥♦ ❞♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s✱ ♣♦r ❢♦r♠❛ ❛ ♦❜t❡r ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ q✉❡ s❡❥❛ r❡♣r❡s❡♥t❛t✐✈❛ ❞❛ s✐♥✐str❛❧✐❞❛❞❡ ♦❜s❡r✈❛❞❛ ♥❛ ❝❛rt❡✐r❛ ❞❡ ❘❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❈✐✈✐❧ ❞♦ ❘❛♠♦ ❆✉t♦♠ó✈❡❧ ❞❛ ●❛r❛♥t✐❛✳

  ◆❛ s❡❣✉♥❞❛ s❡❝çã♦ ❞❡✜♥❡✲s❡ ♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❡♠ ✈✐❣♦r ♥❛ ●❛r❛♥t✐❛✱ ♦❜t❡♥❞♦✲s❡ ❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ ✉s❛♥❞♦ ♦s ♠♦❞❡❧♦s ❛❜❡rt♦ ❡ ❢❡❝❤❛❞♦✱ ❛ ♣❛rt✐r ❞❛s q✉❛✐s sã♦ ❞❡t❡r♠✐♥❛❞❛s ❛s ❡s❝❛❧❛s ó♣t✐♠❛s ❞❡ ♣ré♠✐♦s ♣❛r❛ ♦s ❞♦✐s ♠♦❞❡❧♦s✳ ❈♦♠ ❜❛s❡ ♥❛s ❡s❝❛❧❛s ó♣t✐♠❛s s❡rã♦ ♦❜t✐❞❛s ❛s ♠❡❞✐❞❛s ❞❡ ❛✈❛❧✐❛çã♦ ♣r♦♣♦st❛s ♣♦r ❢❛③❡♥❞♦ ❛✐♥❞❛ ✉♠❛ ❛♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❡♥tr❡ ♦s ❞♦✐s ♠♦❞❡❧♦s✳

  ◆❛ t❡r❝❡✐r❛ s❡❝çã♦ é ❛♣r❡s❡♥t❛❞♦ ✉♠ ♥♦✈♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ♣❛r❛ ❛ ●❛r❛♥t✐❛✱ ♦ q✉❛❧ ❢♦✐ ♣r♦♣♦st♦ ♣❡❧❛ ♠❡s♠❛ ❙❡❣✉r❛❞♦r❛ ❝♦♠ ❜❛s❡ ♥♦ ❞♦❝✉♠❡♥t♦ ❛♣r❡s❡♥t❛❞♦ ♣♦r ◆❡st❛ s❡❝çã♦ sã♦ ❡st✐♠❛❞❛s ❛s ❡s❝❛❧❛s ó♣t✐♠❛s ❞❡ ♣ré♠✐♦s ❜❡♠ ❝♦♠♦ ❛s ♠❡❞✐❞❛s ❞❡ ❛✈❛❧✐❛çã♦ ❝♦rr❡s♣♦♥❞❡♥t❡s ❛♦ ♥♦✈♦ s✐st❡♠❛✱ t❛❧ ❝♦♠♦ ❤❛✈✐❛ s✐❞♦ ❢❡✐t♦ ♣❛r❛ ♦ s✐st❡♠❛ ❛❝t✉❛❧✳

  ◆❛ q✉❛rt❛ s❡❝çã♦ é r❡❛❧✐③❛❞❛ ✉♠❛ ❛♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❡♥tr❡ ♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❛❝t✉❛❧♠❡♥t❡ ❡♠ ✈✐❣♦r ❡ ♦ s✐st❡♠❛ ♣r♦♣♦st♦✱ ❡✈✐❞❡♥❝✐❛♥❞♦ ❛s ❞✐❢❡r❡♥ç❛s ❡♥tr❡ ❡❧❡s✳

  ❖s r❡s✉❧t❛❞♦s ❛♣r❡s❡♥t❛❞♦s ❛♦ ❧♦♥❣♦ ❞♦ t❡r❝❡✐r♦ ❝❛♣ít✉❧♦ ❢♦r❛♠ ♦❜t✐❞♦s r❡❝♦rr❡♥❞♦ ❛♦ s♦❢t✇❛r❡ ▼❛t❤❡♠❛t✐❝❛ ✻✳✵ ❞❛ ❲♦❧❢r❛♠✳

  ❈❛♣ít✉❧♦ ✶ ❙✐st❡♠❛s ❞❡ ❇♦♥✉s ▼❛❧✉s

  ❯♠ ❞♦s ♣r♦❜❧❡♠❛s ❝❡♥tr❛✐s ❞❛ ❛❝t✐✈✐❞❛❞❡ s❡❣✉r❛❞♦r❛ ❝♦♥s✐st❡ ♥❛ ❛✈❛❧✐❛çã♦ ❡✜❝✐❡♥t❡ ❞♦ r✐s❝♦ ❛ss✉♠✐❞♦✱ ❞❡ ❢♦r♠❛ ❛ ❞❡t❡r♠✐♥❛r ♦ ♠♦♥t❛♥t❡ ❛ ♣❛❣❛r ♣❡❧♦ s❡❣✉r❛❞♦✱ ♦ q✉❛❧ s❡ ❝♦♥✈❡♥❝✐♦♥♦✉ ❞❡♥♦♠✐♥❛r ♣♦r ♣ré♠✐♦✳ ❉❛❞♦ q✉❡ ♦ ♣ré♠✐♦ é ✉♠❛ ❝♦♥tr❛♣❛rt✐❞❛ ❞♦ r✐s❝♦ ❛ss✉♠✐❞♦ ♣❡❧❛ s❡❣✉r❛❞♦r❛✱ ❡st❡ t❡rá ❞❡ s❡r✱ s✐♠✉❧t❛♥❡❛♠❡♥t❡✱ ❥✉st♦ ♣❛r❛ ♦ s❡❣✉r❛❞♦ ❡ ✏❧✉❝r❛t✐✈♦✑ ♣❛r❛ ❛ s❡❣✉r❛❞♦r❛✳

  ◆❛ t❛r✐❢❛çã♦✱ ♣r♦❝✉r❛✲s❡ ♠❡❞✐r ♦s ❢❛❝t♦r❡s q✉❡ ✐♥✢✉❡♥❝✐❛♠ ♦ r✐s❝♦✱ ❞❡ ❢♦r♠❛ ❛ ❛❣r✉♣á✲❧♦s ❡♠ ❝❧❛ss❡s ♠❛✐s ♦✉ ♠❡♥♦s ❤♦♠♦❣é♥❡❛s ♣❛r❛ q✉❡✱ ❛ s❡❣✉r❛❞♦s ❝♦♠ ❝❛r❛❝✲ t❡ríst✐❝❛s s❡♠❡❧❤❛♥t❡s s❡❥❛♠ ❛tr✐❜✉í❞♦s ♦ ♠❡s♠♦ ♣ré♠✐♦✱ ♣♦rt❛♥t♦✱ ❝❛❞❛ ❝❧❛ss❡ ❞❡ r✐s❝♦ r❡♣r❡s❡♥t❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ ✉♠ t✐♣♦ ❞❡ s❡❣✉r❛❞♦s✳ ◆♦ s❡❣✉r♦ ❞❡ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❝✐✈✐❧ ❞♦ r❛♠♦ ❛✉t♦♠ó✈❡❧✱ ♣♦r ❡①❡♠♣❧♦✱ ❛s ✈❛r✐á✈❡✐s ♠❛✐s ✉s❛❞❛s ❛ ♣r✐♦r✐ ♣❛r❛ ❞✐❢❡r❡♥❝✐❛r ♦ r✐s❝♦ sã♦✿ ❛ ✐❞❛❞❡ ❞♦ ❝♦♥❞✉t♦r✱ ♦s ❛♥♦s ❞❡ ❝❛rt❛✱ ❛ ③♦♥❛ ❞❡ r❡s✐❞ê♥❝✐❛✱ ♦ s❡①♦ ❞♦ ❝♦♥❞✉t♦r✱ ❛ ❝✐❧✐♥❞r❛❞❛ ❞♦ ✈❡í❝✉❧♦✱ ♦ t✐♣♦ ❞❡ ✈❡í❝✉❧♦✳ ❊st❛s ✈❛r✐á✈❡✐s sã♦ ❞❡s✐❣♥❛❞❛s ♣♦r ✈❛r✐á✈❡✐s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❛ ♣r✐♦r✐✳ ❍á ♠✉✐t❛s ♦✉tr❛s ✈❛r✐á✈❡✐s q✉❡ ✐♥✢✉❡♥❝✐❛♠ ♦ r✐s❝♦✱ ❡ q✉❡ ♥♦ ❡♥t❛♥t♦ ♥ã♦ sã♦ ✐♥❝❧✉í❞❛s ♣♦r ❞✐✈❡rs♦s ♠♦✲ t✐✈♦s✱ ♣♦r ❡①❡♠♣❧♦✱ ❛❧❣✉♠❛s ♣♦rq✉❡ ♥ã♦ sã♦ ♦❜s❡r✈á✈❡✐s ❞✐r❡❝t❛♠❡♥t❡ ✭❛ r❛♣✐❞❡③ ❞♦s r❡✢❡①♦s✱ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞♦ ❝ó❞✐❣♦ ❞❡ ❡str❛❞❛✱ ❛ ❛❣r❡ss✐✈✐❞❛❞❡ ❛♦ ✈♦❧❛♥t❡✱ ❝♦♠♣♦rt❛✲ ♠❡♥t♦s ❛❧❝♦ó❧✐❝♦s✱ ❡t❝✳✮✱ ♦✉tr❛s ♣♦rq✉❡ ♥ã♦ sã♦ ♣♦❧✐t✐❝❛♠❡♥t❡ ❛❞❡q✉❛❞♦s ✭ ♣♦r ❡①❡♠♣❧♦ ❛ ♥❛❝✐♦♥❛❧✐❞❛❞❡✮✱ ♦✉tr❛s ❛✐♥❞❛ ♣♦rq✉❡ ❛ s✉❛ ✐♥❝❧✉sã♦ t♦r♥❛r✐❛ ♦ s✐st❡♠❛ ❞❡♠❛s✐❛❞♦ ❝♦♠♣❧❡①♦✱ ❡t❝✳ ❆ ❡①❝❧✉sã♦ ❞❡ss❛s ✈❛r✐á✈❡✐s ❣❡r❛ ✉♠❛ ❝❡rt❛ ❤❡t❡r♦❣❡♥❡✐❞❛❞❡ ❞❡♥tr♦ ❞❡ ❝❛❞❛ ❝❧❛ss❡ ❞❡ r✐s❝♦ q✉❡ só é ♥♦t❛❞❛ ♣❡❧❛ s❡❣✉r❛❞♦r❛ ❛ ♣♦st❡r✐♦r✐✱ t♦r♥❛♥❞♦ ♦ s✐st❡♠❛ ❞❡s✐❣✉❛❧✳ ❊①✐st❡♠ ♠✉✐t♦s ❡st✉❞♦s✱ ✉♠ ♣♦✉❝♦ ♣♦r t♦❞❛ ❛ ♣❛rt❡✱ q✉❡ ❛✜r♠❛♠ q✉❡ ❡ss❛s ✈❛r✐á✈❡✐s t❡♥❞❡♠ ❛ s❡r ❛s ♠❛✐s ✐♠♣♦rt❛♥t❡s✱ ♦✉ s❡❥❛✱ ♦ ♠❡❧❤♦r ♣r❡❞✐❝t♦r ♣❛r❛ ♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s ❢✉t✉r♦s ♥ã♦ é ❛ ✐❞❛❞❡ ❞♦ ❝♦♥❞✉t♦r✱ ♦s ❛♥♦s ❞❡ ❝❛rt❛✱ ❛ ❝✐❧✐♥❞r❛❞❛ ❞♦ ✈❡í❝✉❧♦✱ ❡t❝✳✱ ♠❛s s✐♠ ❛ s✉❛ ❡①♣❡r✐ê♥❝✐❛ ♣❛ss❛❞❛✳ ❙✉r❣❡ ❛ss✐♠ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ r❡❝t✐✜❝❛r ❛ ♣♦s✲ t❡r✐♦r✐ ♦ ♣ré♠✐♦ ❡♠ ❢✉♥çã♦ ❞❛ s✐♥✐str❛❧✐❞❛❞❡✳ ❊①✐st❡♠ ✈ár✐❛s ♣rát✐❝❛s ❞❡ t❛r✐❢❛çã♦ ❛ ♣♦st❡r✐♦r✐✱ t❛✐s ❝♦♠♦✱ ✏❊①♣❡r✐❡♥❝❡ ❘❛t✐♥❣✑✱ ✏◆♦ ❈❧❛✐♠ ❉✐s❝♦✉♥t✑✱ ✏❙✐st❡♠❛s ❞❡ ❇♦♥✉s ♦✉ ❞❡ ❇♦♥✉s ▼❛❧✉s✑✳ ❚♦❞❛s ❡st❛s ♣rát✐❝❛s ❞❡ t❛r✐❢❛çã♦ ❛ ♣♦st❡r✐♦r✐✱ ❛❣r❛✈❛♠ ♦ ♣ré♠✐♦ ❞♦ s❡❣✉r❛❞♦ ❝❛s♦ ❡st❡ ❞❡❝❧❛r❡ s✐♥✐str♦s ✲ ♠❛❧✉s ✲ ❡ ❜♦♥✐✜❝❛♠ ♦ ♣ré♠✐♦ ❝❛s♦ ♥ã♦ ❞❡❝❧❛r❡ s✐♥✐str♦s ✲ ❜♦♥✉s✳

  ✹ ❈❛♣ít✉❧♦ ✶✳ ❙✐st❡♠❛s ❞❡ ❇♦♥✉s ▼❛❧✉s

  ❝♦♠✉♥✐❞❛❞❡ ❛❝t✉❛r✐❛❧✱ ♣♦✐s ❝♦♥tr❛r✐❛ ♦ ♣r✐♥❝í♣✐♦ ❢✉♥❞❛♠❡♥t❛❧ ❞❛ ❛❝t✐✈✐❞❛❞❡ s❡❣✉r❛❞♦r❛✱ q✉❡ ❝♦♥s✐st❡ ❡♠ ❛❣r✉♣❛r ♦s ✈ár✐♦s r✐s❝♦s ❡♠ ❝❧❛ss❡s ♠❛✐s ♦✉ ♠❡♥♦s ❤♦♠♦❣é♥❡❛s✱ ❞❡ ❢♦r♠❛ ❛ q✉❡ ❛ s❡❣✉r❛❞♦r❛✱ ❜❛s❡❛❞❛ ♥❛ ❧❡✐ ❞♦s ❣r❛♥❞❡s ♥ú♠❡r♦s✱ ❛ss✉♠❛ ❛ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ♠❡❞✐❛♥t❡ ❛ ❛tr✐❜✉✐çã♦ ❞❡ ✉♠ ♣ré♠✐♦ ❝♦♥st❛♥t❡✳ ❈♦♠ ❛ t❛r✐❢❛çã♦ ❛ ♣♦st❡r✐♦r✐✱ ♦ ♣ré♠✐♦ é ❝❛❧❝✉❧❛❞♦ ❡♠ ❢✉♥çã♦ ❞❛ ❡①♣❡r✐ê♥❝✐❛ ♣❛ss❛❞❛ ❞❡ ❝❛❞❛ s❡❣✉r❛❞♦✱ ♣♦rt❛♥t♦ ♦ ♣ré♠✐♦ é ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ q✉❡ ♥ã♦ ❞❡♣❡♥❞❡ ❞♦ ❝♦❧❡❝t✐✈♦✳ ▼❡s♠♦ ❝♦♠ ❡st❛s ❝♦♥tr❛❞✐çõ❡s✱ ♦ s✐st❡♠❛ ❢♦✐ ♠✉✐t♦ ❜❡♠ ❛❝❡✐t❡ ♣❡❧♦ ♣ú❜❧✐❝♦ ❜❡♠ ❝♦♠♦ ❡♥t✐❞❛❞❡s r❡❣✉❧❛❞♦r❛s ❡ ❛❧❛r❣❛❞♦ ❛ ♠✉✐t♦s ♣❛ís❡s✳

  ❯♠❛ ❞❛s ♣r✐♥❝✐♣❛✐s ✈❛♥t❛❣❡♥s ❞❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❡st❡ s✐st❡♠❛ ❞❡ t❛r✐❢❛çã♦ ❝♦♥s✐st❡ ♥♦ ❢❛❝t♦ ❞❡ q✉❡✱ ❛ ❧♦♥❣♦ ♣r❛③♦✱ ❝❛❞❛ s❡❣✉r❛❞♦ ♣❛❣❛rá ♦ ♣ré♠✐♦ ❝♦rr❡s♣♦♥❞❡♥t❡ à s✉❛ ♣ró♣r✐❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ ♦ q✉❡✱ ✐♠♣❧✐❝✐t❛♠❡♥t❡✱ ✐♥❝❡♥t✐✈❛ ❛ ♣rát✐❝❛ ❞❡ ✉♠❛ ❝♦♥❞✉çã♦ ❝❛✉t❡❧♦s❛ ♣♦r ♣❛rt❡ ❞♦ s❡❣✉r❛❞♦✳

  ❙❡❣✉✐♥❞♦ ✐♥tr♦❞✉③✐r❡♠♦s r❡s✉❧t❛❞♦s ❣❡r❛✐s s♦❜r❡ s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s ❡♠ ❝❛rt❡✐r❛s ❢❡❝❤❛❞❛s✳

  ✶✳✶ ●❡♥❡r❛❧✐❞❛❞❡s

  ❖ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s é✱ ❝♦♠♦ s❛❜✐❞♦✱ ✉♠ s✐st❡♠❛ ❞❡ t❛r✐❢❛çã♦ ❛ ♣♦st❡r✐♦r✐✱ ❡♠ q✉❡ ♦ ♣ré♠✐♦✱ ♦❜t✐❞♦ ❡♠ ❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s ❞❡❝❧❛r❛❞♦s✱ é ❛❣r❛✈❛❞♦ ♦✉ ❜♦♥✐✜✲ ❝❛❞♦ ❝♦♥s♦❛♥t❡ ♦ s❡❣✉r❛❞♦ ❞❡❝❧❛r❡ ♦✉ ♥ã♦ s✐♥✐str♦s✳

  ❯♠ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s é ❝❛r❛❝t❡r✐③❛❞♦ ♣❡❧❛s s❡❣✉✐♥t❡s ❝♦♥❞✐çõ❡s✿ ✶✳ ❖s ♣❡rí♦❞♦s ❞❡ ✈✐❣ê♥❝✐❛ ❞♦s ♣ré♠✐♦s sã♦ ❞❡ ✐❣✉❛❧ ❞✉r❛çã♦✱ ❣❡r❛❧♠❡♥t❡ ✉♠ ❛♥♦❀ 1 s , . . . , C ✷✳ ❆s ❛♣ó❧✐❝❡s ❡stã♦ ❞✐✈✐❞✐❞❛s ❡♠ ✉♠ ♥ú♠❡r♦ ✜♥✐t♦ ❞❡ ❝❧❛ss❡s C ❡♠ q✉❡ s

  é ♦ ♥ú♠❡r♦ ❞❡ ❝❧❛ss❡s✳ ❆ ❛♣ó❧✐❝❡ ♠❛♥té♠✲s❡ ♥♦ ♠❡s♠♦ ❡st❛❞♦ ❞✉r❛♥t❡ ♦ ♣❡rí♦❞♦ ❞❡ ✈✐❣ê♥❝✐❛✱ ❣❡r❛❧♠❡♥t❡ ✉♠ ❛♥♦❀

  ✸✳ ❆ ❝❧❛ss❡ ♦♥❞❡ ✉♠ s❡❣✉r❛❞♦ s❡ ❡♥❝♦♥tr❛ ♥♦ ✐♥í❝✐♦ ❞❡ ❝❛❞❛ ♣❡rí♦❞♦ ❞❡♣❡♥❞❡ ✉♥✐✲ ❝❛♠❡♥t❡ ❞❛ ❝❧❛ss❡ ♦♥❞❡ ❡st❡✈❡ ❛♥t❡r✐♦r♠❡♥t❡ ❡ ❞♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s ❞❡❝❧❛r❛❞♦s ♥❡ss❡ ♠❡s♠♦ ♣❡rí♦❞♦✳

  ❖ s✐st❡♠❛ é ❞❡✜♥✐❞♦ ♣♦r três ❡❧❡♠❡♥t♦s✿ T ✶✳ ❆ ❡s❝❛❧❛ ❞❡ ♣ré♠✐♦s b = (b(1), . . . , b(s)) ✳ ❆♣❡s❛r ❞❡st❛ ❞❡s✐❣♥❛çã♦✱ b(i) ♥ã♦ é ♦ i

  ♣ré♠✐♦ ❛♣❧✐❝❛❞♦ à ❝❧❛ss❡ C ♠❛s s✐♠ ♦ ❢❛❝t♦r ♠✉❧t✐♣❧✐❝❛t✐✈♦ ❛ ❛♣❧✐❝❛r ❛♦ ♣ré♠✐♦ i ❛ ♣r✐♦r✐ ❞❛ ❝❧❛ss❡ C ✳ i

  ✷✳ ❆ ❝❧❛ss❡ ❞❡ ❡♥tr❛❞❛✱ C ✱ ♦♥❞❡ ❣❡r❛❧♠❡♥t❡ sã♦ ❝♦❧♦❝❛❞♦s t♦❞♦s ♦s ♥♦✈♦s s❡❣✉r❛❞♦s✳ ✸✳ ❆ ♠❛tr✐③ ❞❡ tr❛♥s✐çã♦ ❞♦ s✐st❡♠❛✱ T ✱ ♦♥❞❡ s❡ ❞❡✜♥❡♠ ❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦ ❞❡

  ✉♠❛ ❝❧❛ss❡ ♣❛r❛ ♦✉tr❛ ♥♦ ✐♥✐❝✐♦ ❞❡ ❝❛❞❛ ♣❡rí♦❞♦✱ ❝♦♥❤❡❝✐❞♦ ♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s ❞♦ ♣❡rí♦❞♦ ❛♥t❡r✐♦r✳ ❆s r❡❣r❛s ❞❡ tr❛♥s✐çã♦✱ T ✱ ♣♦❞❡♠ s❡r ❡s❝r✐t❛s ❝♦♠♦ ✉♠❛

  ✶✳✷ ▼♦❞❡❧♦ ❈❧áss✐❝♦ ✲ ❉✐str✐❜✉✐çã♦ ▲✐♠✐t❡ k ✺ ❆s r❡❣r❛s ❞❡ tr❛♥s✐çã♦ ♣♦❞❡♠ s❡r ❡s❝r✐t❛s ♥❛ ❢♦r♠❛ ❞❡ tr❛♥s❢♦r♠❛çõ❡s T ✱ t❛❧ q✉❡

  T (i) = j k i j s❡ ♦ s❡❣✉r❛❞♦ q✉❡ s❡ ❡♥❝♦♥tr❛ ♥❛ ❝❧❛ss❡ C tr❛♥s✐t❛r ♣❛r❛ ❛ ❝❧❛ss❡ C ✱ s❛❜❡♥❞♦ (k) = t q✉❡ ❞❡❝❧❛r♦✉ k s✐♥✐str♦s✳ P♦❞❡ ❛✐♥❞❛ s❡r ❡s❝r✐t♦ ♥❛ ❢♦r♠❛ ♠❛tr✐❝✐❛❧ T k ♦♥❞❡ (k) (k) ij t = 1 (i) = j = 0 k ij ij s❡ T ❡ t ❝❛s♦ ❝♦♥trár✐♦✳ i , T )

  ❖ s✐st❡♠❛ ♣♦❞❡ s❡r r❡♣r❡s❡♥t❛❞♦ ♣❡❧♦ tr✐♦ (b, C ✳ ❊st❡ tr✐♦✱ q✉❡ ❞❡✜♥❡ ♦ s✐s✲ t❡♠❛✱ s❡rá ❞❡♥♦t❛❞♦ ♣♦r ∆✳ ❙❡♥❞♦ Z ∆,n ❛ ✈✳❛✳ q✉❡ r❡♣r❡s❡♥t❛ ❛ ❝❧❛ss❡ ❞♦ s✐st❡♠❛ ♦♥❞❡ s❡ ❡♥❝♦♥tr❛ ✉♠❛ ❛♣ó❧✐❝❡ ♥♦ ♣❡rí♦❞♦ n✱ ♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ∆ ❢♦r♥❡❝❡ ✉♠❛ ❜❛s❡ ❞❡ t❛r✐❢❛çã♦ ♣❛r❛ Z ∆,n ✱ ❞❛❞❛ ♣❡❧❛ r❡❣r❛s ❞❡ tr❛♥s✐çã♦ T ❡ ♣❡❧❛ ❝❧❛ss❡ ✐♥✐❝✐❛❧ C i ✳ ❯♠❛ ❞❛s ♣r✐♥❝✐♣❛✐s ✈❛♥t❛❣❡♥s ❞♦ s✐st❡♠❛ ❛ss✐♠ ❞❡✜♥✐❞♦ ♣❛r❛ ❛s s❡❣✉r❛❞♦r❛s✱ é ♦ ❢❛❝t♦ ❞❡ ♥ã♦ s❡r ♥❡❝❡ssár✐♦ ❣✉❛r❞❛r ❛ ✐♥❢♦r♠❛çã♦ ❞♦s s✐♥✐str♦s ❞❡❝❧❛r❛❞♦s ♣❡❧♦s s❡❣✉r❛❞♦s ♥♦s ❛♥♦s ❛♥t❡r✐♦r❡s✱ ✐st♦ ♣♦rq✉❡✱ ♣❛r❛ s❛❜❡r♠♦s ♣❛r❛ q✉❡ ❝❧❛ss❡ ♦ s❡❣✉r❛❞♦ s❡ ❞✐r✐❣❡ só é ♥❡❝❡ssár✐❛ ❛ ✐♥❢♦r♠❛çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s ❞❡❝❧❛r❛❞♦s ♥♦ ❛♥♦ ❡ ❛ ❝❧❛ss❡ ❡♠ q✉❡ s❡ ❡♥❝♦♥tr❛ ♥♦ ❛♥♦ ✈✐❣❡♥t❡✳ ◆❡st❛s ❝♦♥❞✐çõ❡s✱ ♦ ♣r♦❝❡ss♦ é ❝❤❛♠❛❞♦ ❞❡ ♣r♦❝❡ss♦ s❡♠ ♠❡♠ór✐❛✱ ♣♦❞❡♥❞♦ ♣♦rt❛♥t♦✱ s❡r tr❛t❛❞♦ ❝♦♠♦ ✉♠❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈✳ ◆❡st❡ ❞♦❝✲ ✉♠❡♥t♦ ❝♦♥s✐❞❡r❛✲s❡ q✉❡ ❛s ❝❛❞❡✐❛s ❞❡ ▼❛r❦♦✈ ✐♠♣❧í❝✐t❛s ♥♦ ♠♦❞❡❧♦ sã♦ ❤♦♠♦❣é♥❡❛s✱ ✐st♦ é✱ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ s❡❣✉r❛❞♦ q✉❡ s❡ ❡♥❝♦♥tr❛ ♥❛ ❝❧❛ss❡ i ❞✐r✐❣✐r ♣❛r❛ ❛ ❝❧❛ss❡ j

  é ✐♥❞❡♣❡♥❞❡♥t❡ ❞♦ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦✳ T ,λ ❉❛❞♦ λ ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✱ s❡❥❛ P ❛ ♠❛tr✐③ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ i tr❛♥s✐çã♦ ❞♦ SBM✳ ❆ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠❛ ❛♣ó❧✐❝❡ q✉❡ s❡ ❡♥❝♦♥tr❛ ♥❛ ❝❧❛ss❡ C j tr❛♥s✐t❛r ♣❛r❛ ❛ ❝❧❛ss❡ C ♥✉♠ ♣❛ss♦ é ❞❛❞❛ ♣♦r✿ p T (i, j) = P[Z = j|Z = i, Λ = λ] i, j = 1, . . . , s. ,λ ∆,n+1 ∆,n

  ❝♦♠ Λ ❛ ✈✳❛✳ q✉❡ r❡♣r❡s❡♥t❛ ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✳ ❆ ❞✐str✐❜✉✐çã♦ Z ∆,n é ❞❛❞❛ ♣♦r (n) p (j) = P(Z = j|Λ = λ), j = 1, . . . , s. ∆,λ ∆,n i ✭✶✳✶✮ q✉❡✱ ♣❛r❛ ❛❧é♠ ❞❡ ❞❡♣❡♥❞❡r ❞❡ T ✱ ❞❡♣❡♥❞❡ t❛♠❜é♠ ❞❛ ❝❧❛ss❡ ✐♥✐❝✐❛❧ C ✳

  ✶✳✷ ▼♦❞❡❧♦ ❈❧áss✐❝♦ ✲ ❉✐str✐❜✉✐çã♦ ▲✐♠✐t❡

  ❖ ♠♦❞❡❧♦ ♣❛r❛ ♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❜❛s❡❛❞♦ ♥❛s ❝❛❞❡✐❛s ❞❡ ▼❛r❦♦✈ ❝♦♥s✐❞❡r❛ q✉❡ ❛ ❝❛rt❡✐r❛ ❞❛s ❛♣ó❧✐❝❡s é ❢❡❝❤❛❞❛✱ ✐st♦ é✱ ♥ã♦ ❛❞♠✐t❡ ❡♥tr❛❞❛s ♥❡♠ s❛í❞❛s ❞❡ ❛♣ó❧✐❝❡s ♥♦ s✐st❡♠❛✳ ❊st❛ ❤✐♣ót❡s❡ é ❡ss❡♥❝✐❛❧ ♣❛r❛ ❛ ❛♣❧✐❝❛çã♦ ❞❡st❡ ♠♦❞❡❧♦✳

  ❙❡ ❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈ ✐♠♣❧í❝✐t❛ ♥♦ s✐st❡♠❛ ❢♦r ✐rr❡❞✉tí✈❡❧✱ ✜♥✐t❛ ❡ ❛♣❡r✐ó❞✐❝❛ ♣♦r✲ t❛♥t♦ r❡❝♦rr❡♥t❡ ♣♦s✐t✐✈❛✱ ✈❡r ♣♦❞❡✲s❡ ❛✜r♠❛r ❡♥tã♦ q✉❡✱ ♣❛r❛ ✉♠❛ ❞❛❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ λ✱ ❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ (n)

  π T (j) = lim p (j), j = 1, . . . , s, n→∞ ∆,λ ✭✶✳✷✮ T ❝♦✐♥❝✐❞❡ ❝♦♠ ❛ ❞✐str✐❜✉✐çã♦ ❡st❛❝✐♦♥ár✐❛ π ✱ ♦✉ s❡❥❛✱ ❝♦♠ ♦ ✈❡❝t♦r ♣ró♣r✐♦ ❡sq✉❡r❞♦ T ,λ T ,λ

  ✻ ❈❛♣ít✉❧♦ ✶✳ ❙✐st❡♠❛s ❞❡ ❇♦♥✉s ▼❛❧✉s

  ♥❡❣❛t✐✈❛ ❞♦ s✐st❡♠❛ ❞❡ ❡q✉❛çõ❡s✿ P π T .P T = π s ,λ ,λ T,λ j=1 π T (j) = 1 P♦rt❛♥t♦✱ ♦❜té♠✲s❡ ❛ss✐♠ ❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ ♣❛r❛ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ λ✳

  

✶✳✸ ❈❛rt❡✐r❛s ❆❜❡rt❛s ✲ ▼♦❞❡❧♦ ❱órt✐❝❡s ❊st♦❝ást✐❝♦s

  ❖ ♠♦❞❡❧♦ ❝❧áss✐❝♦ ❞♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s✱ ❛ss✉♠❡ q✉❡ ❛ ❝❛rt❡✐r❛ ❞❛s ❛♣ó❧✐❝❡s é ❢❡❝❤❛❞❛✱ ❡ q✉❡ ❡①✐st❡ ✉♠❛ ú♥✐❝❛ ❝❧❛ss❡ ❞❡ ❡♥tr❛❞❛ ❞❡ ♥♦✈♦s s❡❣✉r❛❞♦s ♥♦ s✐st❡♠❛✳ ❈♦♠♦ é s❛❜✐❞♦✱ t♦❞♦s ♦s ❛♥♦s ❤á ♥♦✈❛s s✉❜s❝r✐çõ❡s ❡ ❛♥✉❧❛çõ❡s ❞❡ ❛♣ó❧✐❝❡s ♥❛s s❡❣✉r❛❞♦r❛s ♣♦r ❞✐✈❡rs♦s ♠♦t✐✈♦s✱ ❣❡r❛❧♠❡♥t❡ ♣♦rq✉❡ ♦s s❡❣✉r❛❞♦s ❡stã♦ ✐♥s❛t✐s❢❡✐t♦s ❝♦♠ ♦ ✈❛❧♦r ❞♦ ♣ré♠✐♦✱ ❡ ❛❜❛♥❞♦♥❛♠ ❛ s❡❣✉r❛❞♦r❛ à ♣r♦❝✉r❛ ❞❡ ♣ré♠✐♦s ♠❛✐s ❜❛✐①♦s ♦✉ ♠❛✐♦r❡s ❞❡s❝♦♥t♦s ♥✉♠❛ ♦✉tr❛ s❡❣✉r❛❞♦r❛✱ ♦✉ ❡♥tã♦ ♣♦rq✉❡ s✐♠♣❧❡s♠❡♥t❡ ❞❡✐①❛r❛♠ ❞❡ ❝♦♥❞✉③✐r✱ é ♦ ❝❛s♦ ❞♦s ♠❛✐s ✐❞♦s♦s✱ ❡ ❝♦♠♦ ♥ã♦ ❡①✐st❡ ✉♠ ✈í♥❝✉❧♦ ♦❜r✐❣❛tór✐♦ ❝♦♠ ❛ s❡❣✉r❛❞♦r❛✱ q✉❛❧q✉❡r s❡❣✉r❛❞♦ ♣♦❞❡ ❛♥✉❧❛r ❛ ❛♣ó❧✐❝❡ ❡♠ q✉❛❧q✉❡r ❛❧t✉r❛✳ ■st♦ ❢❛③ ❝♦♠ q✉❡ s❡❥❛♠ ♦s r❡st❛♥t❡s s❡❣✉r❛❞♦s q✉❡ ✜❝❛♠ ♥❛ ❝❛rt❡✐r❛ ❛ s✉♣♦rt❛r ♦s ♣r❡❥✉í③♦s ❝❛✉s❛❞♦s✳

  ❆❝t✉❛❧♠❡♥t❡ ❡①✐st❡ ✉♠ ❝❡rt✐✜❝❛❞♦ ❞❡ t❛r✐❢❛çã♦ ♦♥❧✐♥❡✱ ♦♥❞❡ ❛s s❡❣✉r❛❞♦r❛s ♣♦❞❡♠ ✈❡r✐✜❝❛r ♦ ❤✐stór✐❝♦ ❞❡ s✐♥✐str♦s ❞♦s ♥♦✈♦s s❡❣✉r❛❞♦s✱ ♣♦r ❢♦r♠❛ ❛ ❝♦❧♦❝á✲❧♦s ♥❛s ❞✐❢❡r✲ ❡♥t❡s ❝❧❛ss❡s ❞♦ s✐st❡♠❛✳ ◆♦ ❡♥t❛♥t♦✱ ♣♦r ✈❡③❡s ❡st❡ ❝❡rt✐✜❝❛❞♦ é ✐❣♥♦r❛❞♦✱ ♣♦r ❢♦r♠❛ ❛ ♥ã♦ ♣❡♥❛❧✐③❛r ♦s ♥♦✈♦s s❡❣✉r❛❞♦s✱ ♣♦r ♠♦t✐✈♦s ❝♦♠❡r❝✐❛✐s✳ ◆❛s s✐t✉❛çõ❡s ❡♠ q✉❡ ♦ ❝❡rt✐✜❝❛❞♦ é r❡s♣❡✐t❛❞♦✱ ♦ s❡❣✉r❛❞♦ ❡♥tr❛rá ♥❛ ❝❧❛ss❡ ❞❡ ❜♦♥✉s ❝♦rr❡s♣♦♥❞❡♥t❡ ❛♦ s❡✉ ❤✐stór✐❝♦ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ ♣♦❞❡♥❞♦✱ ❛ss✐♠✱ s❡r ❝♦❧♦❝❛❞♦ ❡♠ q✉❛❧q✉❡r ❞❛s ❝❧❛ss❡s ❞♦ s✐st❡♠❛✳ P♦rt❛♥t♦✱ ❛❝t✉❛❧♠❡♥t❡✱ ❢❛③ ♣♦✉❝♦ s❡♥t✐❞♦ ❛ss✉♠✐r q✉❡ ❡①✐st❡ ✉♠❛ ú♥✐❝❛ ❝❧❛ss❡ ❞❡ ❡♥tr❛❞❛ ♥♦ s✐st❡♠❛✳

  ❆❧❣✉♥s ❛✉t♦r❡s tê♠✲s❡ ❞❡❜r✉ç❛❞♦ s♦❜ ♦ ❡st✉❞♦ ❞♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s s♦❜ ❛ ♣❡rs♣❡❝t✐✈❛ ❞❡ ✉♠❛ ❝❛rt❡✐r❛ ❛❜❡rt❛✳ r❡✲ ❢♦r♠✉❧❛♠ ♦ ♣r♦❜❧❡♠❛ ❞♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❜❛s❡❛♥❞♦✲s❡ ♥♦ ♠♦❞❡❧♦ t❡ór✐❝♦ ❛♣r❡✲ s❡♥t❛❞♦ ♣♦r q✉❡ ✈✐s❛ ✉❧tr❛♣❛ss❛r ❛s ❧✐♠✐t❛çõ❡s ❞♦s s✐st❡♠❛s tr❛❞✐❝✐♦♥❛✐s✳ t❛♠❜é♠ ❛♥❛❧✐s❛r❛♠ ♦ SBM ♥✉♠❛ ❝❛rt❡✐r❛ ❛❜❡rt❛✳

  ❆♦ ❧♦♥❣♦ ❞❡st❛ s❡❝çã♦✱ ❛♣r❡s❡♥t❛✲s❡ ♦ ♠♦❞❡❧♦ r❡❢♦r♠✉❧❛❞♦ ♣♦r ❡ ❊st❡s ♠♦❞❡❧♦s ❛♣r❡s❡♥t❛♠ ❛❧t❡r♥❛t✐✈❛s ❞❡ ♠♦❞♦ ❛ ✉❧tr❛♣❛ss❛r ♦s ♣r♦❜❧❡♠❛s ❛♥t❡r✐♦r❡s r❡❢❡r✐❞♦s ❡ ❛ss❡♥t❛♠ ♥❛ t❡♦r✐❛ ❞♦s ✈órt✐❝❡s ❡st♦❝ást✐❝♦s✳

  ❈♦♥s✐❞❡r❡✲s❡ ✉♠❛ ❞❛❞❛ ♣♦♣✉❧❛çã♦✱ q✉❡ ❛❞♠✐t❡ ❡♥tr❛❞❛s ❡ s❛í❞❛s✱ ❞✐✈✐❞✐❞❛ ❡♠ k s✉❜✲ ♣♦♣✉❧❛çõ❡s✱ ♦♥❞❡ ❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ tr❛♥s✐çã♦ ❡♥tr❡ ❛s s✉❜✲♣♦♣✉❧❛çõ❡s✱ ♥✉♠ ♣❡rí♦❞♦✱ ❝♦rr❡s♣♦♥❞❡♠ ❛ ✉♠❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈ ❤♦♠♦❣é♥❡❛✳

  ❉✐③✲s❡ q✉❡ s❡ t❡♠ ✉♠ ✈órt✐❝❡ ❡st♦❝ást✐❝♦ ♥❡ss❛ ♣♦♣✉❧❛çã♦ s❡ ❤♦✉✈❡r ❡st❛❜✐❧✐❞❛❞❡ ♥♦s ❡❢❡❝t✐✈♦s q✉❡ ♦❝✉♣❛♠ ♦s ❡st❛❞♦s tr❛♥s✐❡♥t❡s✳ ❖ s✉♣♦rt❡ ❞♦ ✈órt✐❝❡ é ❝♦♥st✐t✉í❞♦

  ✶✳✸ ❈❛rt❡✐r❛s ❆❜❡rt❛s ✲ ▼♦❞❡❧♦ ❱órt✐❝❡s ❊st♦❝ást✐❝♦s ✼ q✉❡ ♦ ✈órt✐❝❡ s❡ ✐♥st❛❧❛rá✮ ❡ ♦s ❡st❛❞♦s r❡❝♦rr❡♥t❡s ❝♦♥st✐t✉❡♠ ❛s s❛í❞❛s ❞♦ ✈órt✐❝❡✳ ❖ ♠♦❞❡❧♦ ❞♦s ✈órt✐❝❡s ❡st♦❝ást✐❝♦s ♥♦ SBM✱ ❝♦♥s✐❞❡r❛ q✉❡ ❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈ é

  ❝♦♥st✐t✉í❞♦ ♣♦r s ❡st❛❞♦s tr❛♥s✐❡♥t❡s ✭❛s s ❝❧❛ss❡s ❞♦ s✐st❡♠❛✮ ❡ ✉♠ ❡st❛❞♦ ❛❜s♦r✈❡♥t❡ q✉❡ r❡♣r❡s❡♥t❛ ♦ ❡st❛❞♦ ❞❡ s❛í❞❛ ❞♦ s✐st❡♠❛✳ P♦rt❛♥t♦✱ ♦ s✐st❡♠❛ é ❝♦♥st✐t✉í❞♦ ♣♦r s+1 ❡st❛❞♦s✳ ❈♦♥s✐❞❡r❛✲s❡✱ t❛♠❜é♠✱ ✉♠ ✈❡❝t♦r q✉❡ ❝♦♥té♠ ❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ ❡♥tr❛❞❛ ❞❡ ♥♦✈♦s s❡❣✉r❛❞♦s ♣❛r❛ ❛s ❞✐✈❡rs❛s ❝❧❛ss❡s ❞♦ s✐st❡♠❛✱ ♣♦rt❛♥t♦ ♦s ♥♦✈♦s s❡❣✉r❛❞♦s ❡stã♦ s✉❥❡✐t♦s ❛ ✉♠❛ ❝❧❛ss✐✜❝❛çã♦ ✐♥✐❝✐❛❧✱ ♣♦❞❡♥❞♦ s❡r ❝♦❧♦❝❛❞♦s ❡♠ q✉❛❧q✉❡r ✉♠❛ ❞❛s s

  ❝❧❛ss❡s ❞♦ s✐st❡♠❛✳

  ✶✳✸✳✶ ▼❛tr✐③❡s ❞❡ ❚r❛♥s✐çã♦

  ❆❞♠✐t✐♥❞♦ q✉❡ ♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s é ❝♦♥st✐t✉í❞♦ ♣♦r s ❡st❛❞♦s tr❛♥s✐❡♥t❡s ❡ ✶ ❡st❛❞♦ r❡❝♦rr❡♥t❡✱ s❡❥❛♠✿

  • K ✲ ♠❛tr✐③ ❞❡ ❞✐♠❡♥sã♦ s × s✱ ❝✉❥♦s ❡❧❡♠❡♥t♦s r❡♣r❡s❡♥t❛♠ ❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ tr❛♥s✐çã♦ ❡♥tr❡ ❛s ❝❧❛ss❡s tr❛♥s✐❡♥t❡s❀
  • q 1 ✲ ✈❡❝t♦r ❝♦❧✉♥❛✱ ❞❡ ❞✐♠❡♥sã♦ s × 1✱ ❝✉❥♦s ❡❧❡♠❡♥t♦s r❡♣r❡s❡♥t❛♠ ❛s s❛í❞❛s ❞❛s

  ❛♣ó❧✐❝❡s ♥❛s ❝❧❛ss❡s tr❛♥s✐❡♥t❡s✳ ❆ ♠❛tr✐③ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ tr❛♥s✐çã♦✱ ♥✉♠ ♣❛ss♦✱ ❞❛❞❛s ❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦

  T ✱ s❡rá ❞❛❞❛ ♣♦r✿

  K q 1 P T = ✭✶✳✸✮

  1 ❈♦♠♦ s❡ ♣♦❞❡ ♦❜s❡r✈❛r✱ ❛ ú❧t✐♠❛ ❧✐♥❤❛ ❞❛ ♠❛tr✐③ r❡♣r❡s❡♥t❛ ♦ ❡st❛❞♦ ❞❡ s❛í❞❛ ❞❛s ❛♣ó❧✐❝❡s✳

  ❈♦♥s✐❞❡r❡✲s❡ ♦ s❡❣✉✐♥t❡ ❧❡♠❛✿ ▲❡♠❛ ✶✳✶✳ ❆ ♠❛tr✐③ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ tr❛♥s✐çã♦ ❡♠ n ♣❛ss♦s✱ s❡rá ❞❛ ❢♦r♠❛✿ n

  K q n P T ,n =

  ✭✶✳✹✮ P n−1 j

  1 n = K q , n ∈ N 1 ♦♥❞❡ q j=0 ❉❡♠♦♥str❛çã♦✳ ❆ ♣r♦✈❛ é ❢❛❝✐❧♠❡♥t❡ ♦❜t✐❞❛ ♣♦r ✐♥❞✉çã♦ ♠❛t❡♠át✐❝❛ ❡ ♣♦❞❡ s❡r ❝♦♥✲ s✉❧t❛❞❛ ❡♠

  ✶✳✸✳✷ ❋❧✉①♦s ❞❡ ❊♥tr❛❞❛s ♥❛s P♦♣✉❧❛çõ❡s i , i ∈ N

  ❙❡❥❛♠ E ✱ ♦ ♥ú♠❡r♦ t♦t❛❧ ❞❡ ❡♥tr❛❞❛ ❞❡ ♥♦✈♦s s❡❣✉r❛❞♦s ♥♦ i✲és✐♠♦ ❛♥♦✱ ✈❛r✐á✈❡✐s ❛❧❡❛tór✐❛s ✐♥❞❡♣❡♥❞❡♥t❡s✱ ❝♦♠ ❞✐str✐❜✉✐çã♦ P♦✐ss♦♥ ❞❡ ♣❛râ♠❡tr♦ λ i ✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱

  • ❙❡ b = 0✱ ♦ ✢✉①♦ ❞❡ ♥♦✈❛s ❡♥tr❛❞❛s é ❝♦♥st❛♥t❡❀
  • ❙❡ a = 0✱ ♦ ♥ú♠❡r♦ ❞❡ ♥♦✈❛s ❡♥tr❛❞❛s ❡✈♦❧✉✐ ❡♠ ♣r♦❣r❡ssã♦ ❣❡♦♠étr✐❝❛❀
  • ❙❡ a = −b ❡ θ = e δ

  • ❙❡ a = b ❡ θ = e − δ
  • c
  • e

  = 0 ❡ |e

  ✲ ✈❡❝t♦r ❝✉❥❛s ❝♦♠♣♦♥❡♥t❡s tê♠ s♦♠❛ ♥✉❧❛ ❡ sã♦ ✐♥❢❡r✐♦r❡s✱ ❡♠ ♠ó❞✉❧♦✱ às ❝♦♠♣♦♥❡♥t❡s ❝♦rr❡s♣♦♥❞❡♥t❡s ❞❡ c ✱ ✐st♦ é✱ P s j=1 e

  ❀

  ✲ ♦ ✈❡❝t♦r ❡stá✈❡❧✱ ❞❡ ♣❡rí♦❞♦ ♣❛r❛ ♣❡rí♦❞♦✱ t❛❧ q✉❡ c T = ( t T | 0 )

  ✭✶✳✽✮ ♦♥❞❡✿

  ♣♦❞❡rá s❡r r❡♣r❡s❡♥t❛❞♦ ♣♦r c i = c + eγ i , i ∈ N,

  ❖❜s❡r✈❡✲s❡ q✉❡ ❛ ú❧t✐♠❛ ❝♦♠♣♦♥❡♥t❡ ❞❡ c T i ✱ ✐♥❞✐❝❛ q✉❡ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ♥♦✈♦ s❡❣✉r❛❞♦ s❡r ❝♦❧♦❝❛❞♦ ♥♦ ❡st❛❞♦ ❞❡ s❛í❞❛ é ♥✉❧❛✳ ❈♦♥s✐❞❡r❛♥❞♦ q✉❡ ♣♦❞❡rã♦ ❤❛✈❡r ❛❧t❡r❛çõ❡s ♥❛s ❝❧❛ss✐✜❝❛çõ❡s ✐♥✐❝✐❛✐s ❞❡ ❝❛❞❛ ❛♥♦✱ c i

  ✭✶✳✼✮ ♦♥❞❡ t i r❡♣r❡s❡♥t❛ ♦ ✈❡❝t♦r ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ✐♥✐❝✐❛❧ ❞❡ ✉♠ ♥♦✈♦ s❡❣✉r❛❞♦ s❡r ❝♦❧♦❝❛❞♦ ♥♦s ❞✐❢❡r❡♥t❡s ❡st❛❞♦s tr❛♥s✐❡♥t❡s ❞♦ s✐st❡♠❛✳

  = t T i | 0

  ✉♠❛ ❝❧❛ss✐✜❝❛çã♦ ✐♥✐❝✐❛❧✱ ❛✜♠ ❞❡ s❡r❡♠ ❞✐str✐❜✉í❞♦s ♥❛s ❞✐❢❡r❡♥t❡s ❝❧❛ss❡s tr❛♥s✐❡♥t❡s ❞♦ s✐st❡♠❛✱ s❡❥❛ c i ♦ ✈❡❝t♦r ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✐♥✐❝✐❛❧ ♣❛r❛ ♦ ❛♥♦ i✱ i ∈ N✱ ❝♦♠ c T i

  ❞❡ ❡♥tr❛❞❛s ❞❡❝r❡s❝❡♥t❡✳ ❈♦♥s✐❞❡r❛♥❞♦ q✉❡✱ ♥♦ ✐♥í❝✐♦ ❞❡ ❝❛❞❛ ❝♦♥tr❛t♦✱ ♦s ♥♦✈♦s s❡❣✉r❛❞♦s ❡stã♦ s✉❥❡✐t♦s ❛

  , δ > 0 ✱ ♦❜t❡r✲s❡✲á ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❛ss✐♠♣tót✐❝♦ ❝♦♠ ✢✉①♦

  ✢✉①♦ ❞❡ ❡♥tr❛❞❛s ❝r❡s❝❡♥t❡❀

  , δ > 0 ✱ ♦❜t❡r✲s❡✲á ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❛ss✐♠♣tót✐❝♦ ❝♦♠

  ♣❛rt✐❝✉❧❛r✐③❛❞❛✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛s s❡❣✉✐♥t❡s s✐t✉❛çõ❡s✿

  ✭✶✳✻✮ ❆ ❡q✉❛çã♦ r❡♣r❡s❡♥t❛ ♦ ✢✉①♦ ❞❡ ❡♥tr❛❞❛s ❞♦s s❡❣✉r❛❞♦s✳ ❊st❛ ♣♦❞❡ s❡r

  ♦ ❡s♣❛ç♦ ❞❡ ♣❛râ♠❡tr♦s Θ✱ ❝♦rr❡s♣♦♥❞❡ ❛♦s ♣♦ssí✈❡✐s ✈❛❧♦r❡s ❞❡ a✱ b ❡ θ✱ ❞❡✜♥✐❞♦ ♣♦r✿ Θ = {(a, b, θ) : a, θ ∈ R + , b ∈ R, a + bθ > 0} \ {(b, θ) : b ∈ R , θ ∈]1, +∞[}

  ❡ ❡①❝❧✉✐♥❞♦ ♦s ❝❛s♦s ❡♠ q✉❡ (b, θ) ∈ R ×]1, +∞[. P❛r❛ ❢✉t✉r❛s r❡❢❡rê♥❝✐❛s✱ t❛❧ ❝♦♠♦ ❡♠ s❡rá ❝♦♥s✐❞❡r❛❞♦ q✉❡

  ✭✶✳✺✮ s✉❥❡✐t♦ ❛ λ 1 = a + bθ > 0

  ❈♦♥s✐❞❡r❡✲s❡ q✉❡ ❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❡♥tr❛❞❛ ❞❡ ♥♦✈♦s s❡❣✉r❛❞♦s✱ λ i ✱ é ❞❛❞❛ ♣❡❧❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦✿ λ i = a + bθ i , a, θ ∈ R + , b ∈ R, i ∈ N

  ✽ ❈❛♣ít✉❧♦ ✶✳ ❙✐st❡♠❛s ❞❡ ❇♦♥✉s ▼❛❧✉s

  | < |c |, j = 1, . . . , s

  ✶✳✸ ❈❛rt❡✐r❛s ❆❜❡rt❛s ✲ ▼♦❞❡❧♦ ❱órt✐❝❡s ❊st♦❝ást✐❝♦s ✾

  • γ

  ✲ ❡s❝❛❧❛r✱ t❛❧ q✉❡ 0 < γ < 1✳ i ❙❡❥❛ N ✱ i ∈ N✱ ♦ ✈❡❝t♦r q✉❡ ❝♦♥té♠ ♦ ♥ú♠❡r♦ ❞❡ ♥♦✈♦s s❡❣✉r❛❞♦s ♥♦ ✐♥í❝✐♦ ❞♦ i i ∼ P(λ )

  ✲és✐♠♦ ❛♥♦ ♥❛s ✈ár✐❛s ❝❧❛ss❡s ❞❡ ❜♦♥✉s ❞♦ s✐st❡♠❛✳ ❉❛❞♦ q✉❡ E t❡♠✲s❡ i

   i

  ❡♥tã♦ ♦s ❡❧❡♠❡♥t♦s ❞❡ N sã♦ ✈❛r✐á✈❡✐s ❛❧❡❛tór✐❛s ✐♥❞❡♣❡♥❞❡♥t❡s✱ ❝♦♠ ❞✐str✐❜✉✐çã♦ c i,j i,j i ❞❡ P♦✐ss♦♥ ❞❡ ♣❛râ♠❡tr♦ λ i ✱ ❝♦♠ c ❛s ❝♦♠♣♦♥❡♥t❡s ❞♦ ✈❡❝t♦r c ✳ ❈♦♥s✐❞❡r❡✲s❡ ′ ′ λ = λ c i,j i ✳ i,j

  ❖ t❡♦r❡♠❛ s❡❣✉✐♥t❡✱ ❝✉❥❛ ❞❡♠♦♥str❛çã♦ ♣♦❞❡ s❡r ❝♦♥s✉❧t❛❞❛ ❡♠ ♦✉ é ♠✉✐t♦ ✐♠♣♦rt❛♥t❡ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞❡ ❛❧❣✉♥s r❡s✉❧t❛❞♦s ♠❛✐s ❛❞✐❛♥t❡✳ ❚❡♦r❡♠❛ ✶✳✶ ✭❱❡rsã♦ P❛r❛♠étr✐❝❛ ❞♦ ❚❡♦r❡♠❛ ❞❡ ❈❤❛♣♠❛♥✲❑♦❧♠♦❣♦r♦✈✮✳

  , i ∈ N ❈♦♥s✐❞❡r❡✲s❡ ✉♠❛ ♣♦♣✉❧❛çã♦ ❝♦♠ k s✉❜✲♣♦♣✉❧❛çõ❡s✳ ❙❡❥❛ E i ♦ ♥ú♠❡r♦ ❞❡ ❡❧❡✲ i ♠❡♥t♦s ✐♥✐❝✐❛❧♠❡♥t❡ ❝♦❧♦❝❛❞♦s ♥❛ ♣♦♣✉❧❛çã♦ ♥♦ i✲és✐♠♦ ❛♥♦✳ ❆❞♠✐t❡✲s❡ q✉❡ E t❡♠

  ), i ∈ N ❞✐str✐❜✉✐çã♦ P(λ ❡ q✉❡ ❡st❡s ❡❢❡❝t✐✈♦s sã♦ ✐♠❡❞✐❛t❛♠❡♥t❡ ❝❧❛ss✐✜❝❛❞♦s ✭❞✐s✲ i i , i ∈ N tr✐❜✉í❞♦s ♣❡❧❛s s✉❜✲♣♦♣✉❧❛çõ❡s✮ s❡❣✉♥❞♦ ♦ ✈❡❝t♦r ❞❡ ❝❧❛ss✐✜❝❛çã♦ c ✳ P♦st❡r✐✲

  ♦r♠❡♥t❡✱ ♦s ❡❢❡❝t✐✈♦s s❡rã♦ ♣❡r✐♦❞✐❝❛♠❡♥t❡ r❡❝❧❛ss✐✜❝❛❞♦s✱ ❝♦♠ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ tr❛♥✲ s✐çã♦ ❡stá✈❡✐s✱ q✉❡ ❝♦♥st✐t✉❡♠ ❛ ♠❛tr✐③ ❞❡ tr❛♥s✐çã♦ ♥✉♠ ♣❛ss♦ P ✳ ❆♣ós m ♣❡rí♦❞♦s✱ N i,m

  ♦ ♥ú♠❡r♦ ❞❡ ❡❧❡♠❡♥t♦s ♥❛s s✉❜✲♣♦♣✉❧❛çõ❡s ♥♦ m✲és✐♠♦ ❛♥♦✱ ❞❛❞♦ q✉❡ ❡♥tr❛r❛♠ )

  ♥♦ i✲és✐♠♦ ❛♥♦✱ t❡rã♦ s✐❞♦ s✉❥❡✐t♦s ❛ m − i r❡❝❧❛ss✐✜❝❛çõ❡s ❡ t❡rá ❞✐str✐❜✉✐çã♦ P(λ ✱ i,m ❝♦♠ T ′ T m−i λ = λ c P . i,m i i ✭✶✳✾✮

  ❆♦ ✜♠ ❞♦ m✲és✐♠♦ ❛♥♦✱ ❝♦♠ m > i✱ ♦s s❡❣✉r❛❞♦s q✉❡ ❡♥tr❛r❛♠ ♥♦ s✐st❡♠❛ ♥♦ i ✲és✐♠♦ ❛♥♦✱ ❢♦r❛♠ r❡❝❧❛ss✐✜❝❛❞♦s m − i ✈❡③❡s✱ ♣♦rt❛♥t♦✱ ✉t✐❧✐③❛♥❞♦ ♦ t❡♦r❡♠❛ ❛♥t❡r✐♦r✱ t❡♠✲s❡ q✉❡ ♦ ✈❡❝t♦r ❞♦s r❡s♣❡❝t✐✈♦s ❡❢❡❝t✐✈♦s✱ t❡rã♦ ❞✐str✐❜✉✐çã♦ P♦✐ss♦♥ ❞❡ ♣❛râ♠❡tr♦ T m−i ′ T

  λ c P i,m i i ✳ = λ P m ++ ++ = N i,m

  ❈♦♥s✐❞❡r❛♥❞♦ N m ✱ ♦✉ s❡❥❛✱ N m ♦ ♥ú♠❡r♦ t♦t❛❧ ❞❡ s❡❣✉r❛❞♦s ♥♦ i=1 s✐st❡♠❛✱ ♥♦ ✐♥í❝✐♦ ❞♦ m✲és✐♠♦ ❛♥♦✱ ❞❛❞♦ q✉❡ ❥á ❢♦r❛♠ ❝♦♥t❛❜✐❧✐③❛❞❛s ❛s ❡♥tr❛❞❛s ❞♦

  • ++ ++ m ∼ P(λ )

  ✲és✐♠♦ ❛♥♦✱ t❡♠✲s❡ ❡♥tã♦ q✉❡ N m m ✱ ❝♦♠ ++ T ′ T m−i T X m m X λ = λ = λ c P . m i,m i i ✭✶✳✶✵✮ i=1 i=1 Pr♦♣♦s✐çã♦ ✶✳✶✳ ❆♣ós m − i r❡❝❧❛ss✐✜❝❛çõ❡s✱ ♦ ✈❡❝t♦r ♠é❞✐♦ ❞♦ ♥ú♠❡r♦ ❞❡ s❡❣✉r❛❞♦s ♥❛s s✉❜✲♣♦♣✉❧❛çõ❡s s❡rá ❞❛❞♦ ♣♦r T " # ++ X m m ′ m−i ′ T X T

  λ t K t q m i i i i = λ λ . i=1 i=1 m−i ✭✶✳✶✶✮ ❉❡♠♦♥str❛çã♦✳ ❆ ♣r♦✈❛ r❡s✉❧t❛ ❞✐r❡❝t❛♠❡♥t❡ ❞❡ ❡ ♣♦❞❡ s❡r ✈✐st❛ ❡♠

  ❊st❡ r❡s✉❧t❛❞♦ ♣♦❞❡ s❡r ❝♦♥s✉❧t❛❞♦ ❡♠

  β T j ✭✶✳✶✹✮

  K = s X j=1 η j α j β T j ✭✶✳✶✸✮ ♦♥❞❡✿

  λ + T m = m X i=1 λ i t T i K m−i = m X i=1 λ i t T i s X j=1 η m−i j α j β T j = = s X λ i m X g i,j η m−i j !

  ❈♦♠♦ ♦s ✈❡❝t♦r❡s ♣ró♣r✐♦s à ❡sq✉❡r❞❛ ❡ à ❞✐r❡✐t❛ ❝♦rr❡s♣♦♥❞❡♥t❡s ❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ♣ró♣r✐♦s sã♦ ♦rt♦❣♦♥❛✐s✱ ❡ t❡♥❞♦ ❡♠ ❝♦♥t❛ ♦ r❡s✉❧t❛❞♦ t❡♠✲s❡ q✉❡ ♦ ✈❡❝t♦r ♠é❞✐♦ ❞♦s s❡❣✉r❛❞♦s ♥❛s ❝❧❛ss❡s tr❛♥s✐❡♥t❡s✱ ♣❛ss❛❞♦s m ❛♥♦s✱ é ❞❛❞♦ ♣♦r✿

  | < 1, j = 1, . . . , s ✳

  ❆t❡♥❞❡♥❞♦ ❛♦ t❡♦r❡♠❛ ❞❡ P❡rr♦♥ ❋r♦❜❡♥✐✉s ✭♣♦❞❡ s❡r ❝♦♥s✉❧t❛❞♦ ❡♠ s❡ ❛ ♠❛tr✐③ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ tr❛♥s✐çã♦ ♥✉♠ ♣❛ss♦✱ P ✱ ❢♦r ✜♥✐t❛✱ ✐rr❡❞✉tí✈❡❧ ❡ ❛♣❡r✲ ✐ó❞✐❝❛✱ ❡♥tã♦ t❡♠✲s❡ q✉❡✿

  ❀

  ✲ sã♦ ♦s ✈❛❧♦r❡s ♣ró♣r✐♦s ❞❛ ♠❛tr✐③ K✱ t❛❧ q✉❡ |η 1 | > |η 2 | > . . . > |η s |

  ❡✱ ♣♦st❡r✐♦r♠❡♥t❡✱ ❞❡t❡r♠✐♥❛r ❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ ❞♦ s✐st❡♠❛✳ ❊♠ ❝♦♥❞✐çõ❡s ❣❡♥ér✐❝❛s✱ ❛ ♠❛tr✐③ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ tr❛♥s✐çã♦ ❞❛s ❝❧❛ss❡s tr❛♥✲ s✐❡♥t❡s ♣♦❞❡rá s❡r r❡♣r❡s❡♥t❛❞❛✱ ♣♦r ✭✈❡r

  ✶✵ ❈❛♣ít✉❧♦ ✶✳ ❙✐st❡♠❛s ❞❡ ❇♦♥✉s ▼❛❧✉s

  = a+bθ i , (a, b, θ) ∈ Θ

  ✭✶✳✶✷✮ ◆❡st❛ s❡❝çã♦✱ ♣r❡t❡♥❞❡✲s❡ ♣r✐♠❡✐r♦ ♣r♦✈❛r ❛ ❡①✐stê♥❝✐❛ ❞♦ ✈órt✐❝❡ ♥❛s ❝❧❛ss❡s tr❛♥✲ s✐❡♥t❡s✱ ❞❛❞♦ q✉❡ ♦ ✢✉①♦ ❞❡ ❡♥tr❛❞❛ ❞❡ ♥♦✈♦s s❡❣✉r❛❞♦s é ❞❛❞♦ ♣♦r λ i

  λ + T m = m X i=1 λ i t T i K m−i .

  ❆ss✐♠ s❡♥❞♦✱ ❝♦♥s✐❞❡r❛♥❞♦ q✉❡ λ + m é ♦ ✈❡❝t♦r ♠é❞✐♦ ❞♦ ♥ú♠❡r♦ ❞❡ s❡❣✉r❛❞♦s ♥❛s ❝❧❛ss❡s tr❛♥s✐❡♥t❡s ❞♦ s✐st❡♠❛ ♥♦ m✲és✐♠♦ ♣❡rí♦❞♦✱ t❡♠✲s❡ ❡♥tã♦ q✉❡

  ❈♦♠♦ ❢♦✐ ❞✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ s♦❜ ❛ ❤✐♣ót❡s❡ ❞❡ ❡①✐stê♥❝✐❛ ❞❡ ✈órt✐❝❡s✱ ❡st❡s ✐♥st❛❧❛r✲s❡✲ ã♦ ♥❛s ❝❧❛ss❡s tr❛♥s✐❡♥t❡s ❞♦ s✐st❡♠❛✳

  ✶✳✸✳✸ ❉✐str✐❜✉✐çã♦ ▲✐♠✐t❡

  • η j
  • α j sã♦ ♦s ✈❡❝t♦r❡s ♣ró♣r✐♦s ❡sq✉❡r❞♦s ✭♥♦r♠❛❧✐③❛❞♦s✮ ❞❛ ♠❛tr✐③ K❀
  • β j sã♦ ♦s ✈❡❝t♦r❡s ♣ró♣r✐♦s ❞✐r❡✐t♦s ✭♥♦r♠❛❧✐③❛❞♦s✮ ❞❛ ♠❛tr✐③ K✳
  • 1 |
  • j

  ✶✳✸ ❈❛rt❡✐r❛s ❆❜❡rt❛s ✲ ▼♦❞❡❧♦ ❱órt✐❝❡s ❊st♦❝ást✐❝♦s ✶✶ T α i,j j = t , i = 1, . . . , m, j = 1, . . . , s

  ❝♦♠ g i ✳ ❖ s❡❣✉✐♥t❡ ❧❡♠❛ ❡ ♦ s❡✉ ❝♦r♦❧ár✐♦ ♣♦❞❡♠ s❡r ❝♦♥s✉❧t❛❞♦s ❡♠ ❡ s❡r✈❡♠ ♣❛r❛ s✐♠♣❧✐✜❝❛r ❛ ❛♥á❧✐s❡ ❞❛ ❡①✐stê♥❝✐❛ ❞❡ ✈órt✐❝❡s ❡st♦❝ást✐❝♦s ♥❛s ❝❧❛ss❡s tr❛♥✲ s✐❡♥t❡s✳ g i,j = g j , j = 1, . . . , s i,j = g i,j − g j ▲❡♠❛ ✶✳✷✳ ❙❡ lim ✱ ❡ t♦♠❛♥❞♦ d ✱ t❡r✲s❡✲á i→+∞ P m ′ m−i j=0 i j λ d i,j η lim = 0 , j = 1, . . . , s P m m→+∞ m−i ✭✶✳✶✺✮ i=1 λ η i j d = 0

  ❈♦r♦❧ár✐♦ ✶✳✶✳ ❙❡ lim i,j ✱ ❡♥tã♦ i→+∞ P m ′ m−i j=0 i j λ g η i,j lim = 1. P m→+∞ n ′ m−i ✭✶✳✶✻✮ i=1 i j λ η d = 0, j = 1, . . . , s i,j i,j j , j = P♦rt❛♥t♦✱ s❡ lim ✱ ❡♥tã♦ g ♣♦❞❡ s❡r s✉❜st✐t✉í❞♦ ♣♦r g i→+∞ 1, . . . , s

  ✱ ♦ q✉❡ s✐♠♣❧✐✜❝❛rá ❜❛st❛♥t❡ ♦ ❝❛❧❝✉❧♦ ❞♦s ❧✐♠✐t❡s ♣❛r❛ ♦s ♣❛râ♠❡tr♦s ❡ q✉♦✲ ❝✐❡♥t❡s ❞♦s ♣❛râ♠❡tr♦s✳ i

  ❆t❡♥❞❡♥❞♦ à ❞❡✜♥✐çã♦ ❢❡✐t❛ ♣❛r❛ c ❡♠ ♦ ✈❡❝t♦r ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ✐♥✐❝✐❛✐s ♣❛r❛ ♦s ❡st❛❞♦s tr❛♥s✐❡♥t❡s✱ ❝✉❥♦ ❧✐♠✐t❡ s❡rá ❞❛❞♦ ♣♦r i t i→+∞ i→+∞ lim = lim (t + eγ ) = t i

  ❞❛❞♦ q✉❡ 0 < γ < 1✳ ❙❡♥❞♦ ❛ss✐♠✱ t❡♠✲s❡ T T t i→+∞ i→+∞ lim g i,j = lim .α j = t .α j = g j . i d = 0 i,j ▲♦❣♦✱ t❡♠♦s q✉❡ lim ✱ ♣♦rt❛♥t♦ ♦ ▲❡♠❛ ❡ ♦ s❡✉ ❝♦r♦❧ár✐♦ sã♦ ✈❡r✐✜❝❛❞♦s✳ i→+∞ ❈♦♥❢♦r♠❡ r❡❢❡r✐❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ♣r❡t❡♥❞❡✲s❡ ❞❡t❡r♠✐♥❛r ♦ ❧✐♠✐t❡ ❞♦ ✈❡❝t♦r ♠é❞✐♦ +

  ❞♦s s❡❣✉r❛❞♦s ♥❛s ❝❧❛ss❡s tr❛♥s✐❡♥t❡s✱ ♦ q✉❛❧ é ❞❛❞♦ ♣♦r X s m X m−i ! T λ β m i j j = λ g η j=1 i=1 i,j i,j

  ❈♦♠♦ ♦ ▲❡♠❛ ❡ ♦ s❡✉ ❝♦r♦❧ár✐♦ sã♦ ✈❡r✐✜❝❛❞♦s✱ ❡♥tã♦ ♣♦❞❡✲s❡ s✉❜st✐t✉✐r g ♣♦r m m−i g λ g η j j m,j ✳ ❉❡♥♦t❛♥❞♦ P i j ♣♦r u ✱ t❡♠✲s❡ ❡♥tã♦ q✉❡ i=1 X m m m−i i m−i X u m,j = λ g j η = (a + bθ )g j η = i=1 i=1 i m m m j j 1 − η θ − η j j

  = ag + bg j j ✭✶✳✶✼✮

  • ❙❡ 0 < θ < 1❀ lim m→+∞
  • ❙❡ θ = 1 lim m→+∞
  • ❙❡ θ > 1 lim m→∞ u m,j

  ✭✶✳✷✶✮ ♣♦✐s |η| < 1✳

  ✭✶✳✷✹✮ ❈♦♥❝❧✉✐✲s❡ ❛ss✐♠ q✉❡✱ ♣❛r❛ 0 < θ ≤ 1✱ ❡①✐st❡ ❧✐♠✐t❡ ✜♥✐t♦ ♣❛r❛ ♦ ✈❡❝t♦r ❡st✐✲

  β T j .

  = s X j=1 g j b 1 − η j

  λ + T m θ m

  ✭✶✳✷✸✮

  λ + T m = s X j=1 g j (a + b) 1 − η j β T j .

  ✭✶✳✷✷✮

  β T j .

  λ + T m = s X j=1 g j a 1 − η j

  = a + bθ i , i ∈ N, (a, b, θ) ∈ Θ ❡ s❡ lim i→+∞ d i,j = 0, j = 1, . . . , s ✱ t❡♠✲s❡ q✉❡

  ❚❡♠♦s ♣♦rt❛♥t♦✱ ❛ s❡❣✉✐♥t❡ ♣r♦♣♦s✐çã♦ ✭♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞❛ ❡♠ ♦✉ ✿ Pr♦♣♦s✐çã♦ ✶✳✷✳ ❙❡ ❛s ✐♥t❡♥s✐❞❛❞❡s ❞❡ ❡♥tr❛❞❛ ♥❛ ♣♦♣✉❧❛çã♦ sã♦ ♠♦❞❡❧❛❞❛s ♣♦r λ i

  ✭✶✳✷✵✮ ❙❡ θ = η j ✱ ♣❛r❛ ❛❧❣✉♠ j ✱ ✈❡r t❡♠✲s❡ q✉❡ lim m→+∞ u m,j = g j a 1 − η j

  θ − η j , j = 1, . . . , s.

  θ m = g j b

  ✭✶✳✶✾✮

  u m,j = g j (a + b) 1 − η j , j = 1, . . . , s,

  η m+1 j = 0 ✱ ♣♦✐s |η j | < 1.

  θ m+1 = 0 ❡ lim m→+∞

  ✭✶✳✶✽✮ ❞❛❞♦ q✉❡ lim m→+∞

  u m,j = g j a 1 − η j , j = 1, . . . , s,

  ✳ ❚❡♠✲s❡ ❡♥tã♦ q✉❡ ♦ ❧✐♠✐t❡ ❞❡ u m,j ✱ q✉❛♥❞♦ m → ∞✱ ❞❡♣❡♥❞❡ ❞❡ θ ❡ s❡rá ❞❛❞♦ ♣♦r✿

  ❝♦♠ θ 6= η j , j = 1, . . . , s

  ✶✷ ❈❛♣ít✉❧♦ ✶✳ ❙✐st❡♠❛s ❞❡ ❇♦♥✉s ▼❛❧✉s

  • ❙❡ 0 < θ < 1 lim m→+∞
  • ❙❡ θ = 1 lim m→+∞
  • ❙❡ θ > 1 lim m→+∞

  ♠❛❞♦r ❞♦s ♣❛râ♠❡tr♦s✱ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛♦ ✈❡❝t♦r ♠é❞✐♦ ❞♦ ♥ú♠❡r♦ ❞❡ s❡❣✉r❛❞♦s ♥❛s s✉❜✲♣♦♣✉❧❛çõ❡s✳ P❛r❛ θ > 1✱ t❡♠✲s❡ q✉❡ ❛s ❝♦♠♣♦♥❡♥t❡s ❞♦ ✈❡❝t♦r ❡st✐♠❛❞♦r ❞♦s ♣❛râ♠❡tr♦s✱ ❝r❡s❝❡♠ ♣r♦♣♦r❝✐♦♥❛❧♠❡♥t❡ ❛ θ m ♣❛r❛ +∞✳

  • + ✶✳✸ ❈❛rt❡✐r❛s ❆❜❡rt❛s ✲ ▼♦❞❡❧♦ ❱órt✐❝❡s ❊st♦❝ást✐❝♦s ✶✸

  λ m,j π ∞ = lim , j = 1, . . . , s. ,j P s m→+∞ ✭✶✳✷✺✮ + j=1 λ m,j + +

  , j = 1, . . . , s ❝♦♠ λ ❛s ❝♦♠♣♦♥❡♥t❡s ❞♦ ✈❡❝t♦r λ ✳ m,j m

  ❋✐❝❛ ❛ss✐♠ ♣r♦✈❛❞♦ q✉❡✱ ❛ ❧♦♥❣♦ ♣r❛③♦✱ ❡①✐st❡ ❡st❛❜✐❧✐❞❛❞❡ ❞❛ ❞✐♠❡♥sã♦ r❡❧❛t✐✈❛ ❞❛s ❝❧❛ss❡s ❞♦ s✐st❡♠❛✱ ❝❛r❛❝t❡ríst✐❝❛ ❞❛ ❡①✐stê♥❝✐❛ ❞❡ ✈órt✐❝❡s ❡st♦❝ást✐❝♦s✳ ❈♦♥s✐❞❡r❡✲s❡ ❡♥tã♦ ❛ s❡❣✉✐♥t❡ ♣r♦♣♦s✐çã♦✿ Pr♦♣♦s✐çã♦ ✶✳✸✳ ❙❡ ❛s ✐♥t❡♥s✐❞❛❞❡s ❞❡ ❡♥tr❛❞❛s ♣❛r❛ ❛ ♣♦♣✉❧❛çã♦ sã♦ ♠♦❞❡❧❛❞❛s ♣♦r ′ i λ = a + bθ , i ∈ N, (a, b, θ) ∈ Θ i→∞ d i,j = 0, j = 1, . . . , s i ❡ s❡ lim ✱ ❡①✐st❡ ✉♠ ✈órt✐❝❡ ❡st♦❝ást✐❝♦ ♥❛ ♣♦♣✉❧❛çã♦✱ ❝♦♠ s✉♣♦rt❡ ♥♦s ❡st❛❞♦s tr❛♥s✐❡♥t❡s✳

  P❛r❛ 0 < θ ≤ 1✱ ❝♦♥s✐❞❡r❛♥❞♦ q✉❡ ❛s ✐♥t❡♥s✐❞❛❞❡s ❞❡ ❡♥tr❛❞❛s ♥❛ ♣♦♣✉❧❛çã♦ s❡ ′ i = a + bθ , i ∈ N

  ❝♦♠♣♦rt❛♠ ❞❛ ❢♦r♠❛ λ i ✱ ❞✐③✲s❡ q✉❡ s❡ ❡stá ♣❡r❛♥t❡ ♣♦♣✉❧❛çõ❡s ❡st❛❝✐♦♥ár✐❛s✱ ✐st♦ ♣♦rq✉❡ ❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ tr❛♥s✐çã♦ ❡♥tr❡ ❛s s✉❜✲♣♦♣✉❧❛çõ❡s sã♦ ❡stá✈❡✐s✱ ❡ ❛ ❧♦♥❣♦ ♣r❛③♦✱ ✈❡r✐✜❝❛✲s❡ ❡st❛❜✐❧✐❞❛❞❡ ❞❛s ❞✐♠❡♥sõ❡s ❛❜s♦❧✉t❛s ❡ r❡❧❛t✐✈❛s ❞❛s s✉❜✲♣♦♣✉❧❛çõ❡s✳

  P❛r❛ θ > 1✱ ♥❛s ♠❡s♠❛s ❝♦♥❞✐çõ❡s✱ ❞✐③✲s❡ q✉❡ s❡ ❡stá ♣❡r❛♥t❡ ♣♦♣✉❧❛çõ❡s ♠❛❞✉r❛s✱ ✐st♦ ♣♦rq✉❡ ❛♣❡♥❛s ❡①✐st❡ ❡st❛❜✐❧✐❞❛❞❡ ❞❛s ❞✐♠❡♥sõ❡s r❡❧❛t✐✈❛s ❞❛s s✉❜✲♣♦♣✉❧❛çõ❡s✳

  P❛r❛ ❡❢❡✐t♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s✱ s❡rã♦ ✉t✐❧✐③❛❞♦s r❡s✉❧t❛❞♦s ❝♦♥❤❡❝✐❞♦s s♦❜r❡ sér✐❡s ❣❡♦✲ ♠étr✐❝❛s ❞❡ ♠❛tr✐③❡s ✭♣♦r ❡①❡♠♣❧♦✱ ❝♦♥s✉❧t❛r ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛ +T

  • +T m→+∞

  λ m→+∞ λ ❡①♣r❡ssã♦ ❞❡ lim m ✳ ❯t✐❧✐③❛♥❞♦ ❡ss❡s r❡s✉❧t❛❞♦s ❡ ❞❡♥♦t❛♥❞♦ lim m +T ♣♦r λ ∞ ✱ t❡♠✲s❡ q✉❡✿ +T T − 1 P❛r❛ 0 < θ < 1

  • λ = at (I − K)

  ✭✶✳✷✻✮ +T T − 1 P❛r❛ θ = 1

  • λ

  = (a + b)t (I − K) ✭✶✳✷✼✮ +T 1 P❛r❛ θ > 1

  • +T m T

  λ

  1 K λ = lim = bt I − i→+∞ m ✭✶✳✷✽✮

  θ θ θ ♦♥❞❡ I é ❛ ♠❛tr✐③ ✐❞❡♥t✐❞❛❞❡ ❞❡ ❞✐♠❡♥sã♦ s × s✳

  ❖ ✈❡❝t♦r ❧✐♠✐t❡ ❞❛s ❞✐♠❡♥sõ❡s r❡❧❛t✐✈❛s ❞❛s s✉❜✲♣♦♣✉❧❛çõ❡s✱ π ✱ é ❞❡t❡r♠✐♥❛❞♦ + + ❞✐✈✐❞✐♥❞♦ ❝❛❞❛ ❡❧❡♠❡♥t♦ ❞❡ λ ∞ ♦✉ λ ♣❡❧❛ s♦♠❛ ❞❡ t♦❞♦s ♦s ❡❧❡♠❡♥t♦s✱ ❝♦♥s♦❛♥t❡ ∞ ,θ 0 < θ ≤ 1

  ♦✉ θ > 1✱ ♦✉ s❡❥❛✿ P❛r❛ 0 < θ ≤ 1 +

  • λ (j)

  π T (j) = P s ✭✶✳✷✾✮ j=1 λ (j)

  • λ (j)

  P❛r❛ θ > 1 +

  π T (j) = P s ✭✶✳✸✵✮ λ ∞ (j)

  ❈❛♣ít✉❧♦ ✷ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s ❡ ▼❡❞✐❞❛s ❞❡ ❆✈❛❧✐❛çã♦ ❞❡ ❙❇▼ ✷✳✶ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s

  ▼✉✐t♦s ❛✉t♦r❡s✱ ❛♦ ❧♦♥❣♦ ❞♦s t❡♠♣♦s✱ tê♠✲s❡ ❞❡❜r✉ç❛❞♦ s♦❜r❡ ♦ ♣r♦❜❧❡♠❛ ❞❛ ❞❡t❡r✲ ♠✐♥❛çã♦ ❞❡ ♣ré♠✐♦s ❛ ✈✐❣♦r❛r❡♠ ❡♠ ❝❛❞❛ ❝❧❛ss❡ ❞♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s✱ ✉♠❛ ✈❡③ ❞❛❞❛ ❛ ♠❛tr✐③ ❞❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦✳ ❖s ♠♦❞❡❧♦s ♣r♦♣♦st♦s tê♠ ❝♦♠♦ ♦❜❥❡❝t✐✈♦ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ❡s❝❛❧❛s ❞❡ ♣ré♠✐♦s ó♣t✐♠♦s ♣♦r ❢♦r♠❛ ❛ ♦♣t✐♠✐③❛r ❛ ❝❛rt❡✐r❛ ❞❛s ❛♣ó❧✐❝❡s✳

  ❆♦ ❧♦♥❣♦ ❞❡st❡ ❝❛♣ít✉❧♦✱ ❝♦♠ ❜❛s❡ ❡♠ ♣r❡t❡♥❞❡✲s❡ ❛♣r❡s❡♥t❛r ❛❧✲ ❣✉♥s ❞❡ss❡s ♠♦❞❡❧♦s✱ ♣r♦♣♦st♦s ♣♦r ❛❧❣✉♥s ❛✉t♦r❡s✱ ❡ t❛♠❜é♠ ❛❜♦r❞❛r ❛s ♠❡❞✐❞❛s ❞❡ ❡✜❝✐ê♥❝✐❛ ♣♦r ❢♦r♠❛ ❛ ❝♦♠♣❛r❛r ❞✐❢❡r❡♥t❡s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s✳

  ✷✳✶✳✶ ❖ ▼♦❞❡❧♦ ❞❡ ◆♦r❜❡r❣

  ❖ ♠♦❞❡❧♦ ❛♣r❡s❡♥t❛❞♦ ♣♦r ✉t✐❧✐③❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ s❡♠❡❧❤❛♥t❡ à ❚❡♦r✐❛ ❞❡ ❈r❡❞✐❜✐❧✐❞❛❞❡✳

  , n ∈ N ❙❡❥❛♠ S n ♦ ♠♦♥t❛♥t❡ ❞❛s ✐♥❞❡♠♥✐③❛çõ❡s ❛❣r❡❣❛❞❛s r❡❧❛t✐✈❛s ❛ ✉♠ s❡❣✉r❛❞♦

  ♥♦ n✲és✐♠♦ ♣❡rí♦❞♦ ❞❡ ❝♦♥tr❛t♦ ❞❛ ❛♣ó❧✐❝❡✳ ❉❛❞❛ ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ λ✱ n , n ∈ N s✉♣♦♥❤❛✲s❡ q✉❡ S sã♦ ✈❛r✐á✈❡✐s ❛❧❡❛tór✐❛s ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ✐❞❡♥t✐❝❛♠❡♥t❡ ∆,n ❞✐str✐❜✉í❞❛s✳ Z ❞❡s✐❣♥❛✱ ❝♦♠♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ q✉❡ r❡♣r❡s❡♥t❛ ❛ ❝❧❛ss❡ ❡♠ q✉❡ ✉♠❛ ❛♣ó❧✐❝❡ ❣❡♥ér✐❝❛ s❡ ❡♥❝♦♥tr❛ ♥♦ n✲és✐♠♦ ♣❡rí♦❞♦✱ q✉❛♥❞♦ ✈✐❣♦r❛ ♦ i ) s✐st❡♠❛ ∆ = (b, T, C ✳ n ∆,n (Z ) n |λ]

  ❙❡❥❛ b ✉♠ ❡st✐♠❛❞♦r ❞♦ ♣ré♠✐♦ ❞❡ r✐s❝♦ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ E[S ✳ ❆ ♠❡❞✐❞❛ n (Z ∆,n ) ❞❡ ❡✜❝✐ê♥❝✐❛ ❞♦ ♣ré♠✐♦ b ✱ é ❛ ♣❡r❞❛ q✉❛❞rát✐❝❛ ❡s♣❡r❛❞❛ 2 Q (∆) = E E[S |λ] − b (Z ) . n n n ∆,n

  ✭✷✳✶✮ ❊st❛❜❡❧❡❝❡✲s❡ ❝♦♠♦ ♦❜❥❡❝t✐✈♦ ♠✐♥✐♠✐③❛r ❛ ❞✐❢❡r❡♥ç❛ q✉❛❞rát✐❝❛ ❡s♣❡r❛❞❛ ❡♥tr❡ ♦ ♣ré♠✐♦

  ✶✻ ❈❛♣ít✉❧♦ ✷✳ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s ❡ ▼❡❞✐❞❛s ❞❡ ❆✈❛❧✐❛çã♦ ❞❡ ❙❇▼ ∆,n ❉❛❞♦ q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ Z ❞❡♣❡♥❞❡✱ ♣❛r❛ ❛❧é♠ ❞♦s ❡❧❡♠❡♥t♦s r❡❢❡r✐❞♦s✱ ❞♦

  ♣❛râ♠❡tr♦ λ✱ t❡r✲s❡✲á✿ Z ∞ 2 E[S Q (∆) = |λ] − b (Z ) n n n ∆,n Z X s 2 (n) = [E(S |λ) − b(j)] p (j)dU (λ). j=1 n ∆,λ ✭✷✳✷✮ n ∆,n ∆,n (Z )

  ❚❡♦r❡♠❛ ✷✳✶✳ P❛r❛ q✉❛❧q✉❡r b ✱ ❜❛s❡❛❞♦ ❡♠ Z ✱ t❡♠✲s❡ q✉❡ Q (∆) ≥ E[V [E(S |λ)|Z ]] n n ∆,n

  ✭✷✳✸✮ ❝♦♠ ❛ ✐❣✉❛❧❞❛❞❡ ❛ ✈❡r✐✜❝❛r✲s❡ s❡ ❡ só s❡ P

  [b (Z ) = µ (Z )] = 1, n ∆,n n ∆,n ❝♦♠ µ n (Z ∆,n ) = E[E[S n |λ]|Z ∆,n ].

  ✭✷✳✹✮ ❖ ❚❡♦r❡♠❛ ❞❡♠♦♥✲

  (Z ) str❛ q✉❡ µ n ∆,n é ♦ ❡st✐♠❛❞♦r q✉❡ ♠✐♥✐♠✐③❛ ❛ ♣❡r❞❛ q✉❛❞rát✐❝❛ ❡s♣❡r❛❞❛✳ (Z )

  ❖ ❡st✐♠❛❞♦r µ n ∆,n é ♦ ♣ré♠✐♦ ❞❡ ❝r❡❞✐❜✐❧✐❞❛❞❡ ♣❛r❛ ♦ ♣❡rí♦❞♦ n✱ ❜❛s❡❛❞❛ ♥❛ ∆,n n (∆) ❝❧❛ss❡ ❞❡ ❜♦♥✉s ♥❡ss❡ ♣❡rí♦❞♦✱ Z ✳ ◆❛ t❡r♠✐♥♦❧♦❣✐❛ ❇❛②❡s✐❛♥❛✱ Q é ♣r♦♣♦r❝✐✲ n (Z ∆,n ) n |λ] ♦♥❛❧ ❛♦ r✐s❝♦ ❞♦ ❡st✐♠❛❞♦r b ♣❛r❛ E[S ✱ q✉❛♥❞♦ s❡ ✉s❛ ❛ ❢✉♥çã♦ ❞❛ ♣❡r❞❛ n ∆,n (Z ) q✉❛❞rát✐❝❛ ❡ µ ♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❡st✐♠❛❞♦r ❞❡ ❇❛②❡s✳ ◆♦t❡✲s❡ q✉❡

  E[S = E[S E[µ n (Z ∆,n )] = E n |λ] n ],

  ♦ q✉❡ ✐♠♣❧✐❝❛ q✉❡✱ ❡♠ ♠é❞✐❛✱ ♦ ♣ré♠✐♦ ❞❡ ❝r❡❞✐❜✐❧✐❞❛❞❡ ✐❣✉❛❧❛ ❛s ✐♥❞❡♠♥✐③❛çõ❡s ❡s♣❡✲ r❛❞❛s✳ ➚ ♣❛rt✐❞❛✱ ♣♦❞✐❛ ❛✜r♠❛r✲s❡ q✉❡ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦ ♣ré♠✐♦ ó♣t✐♠♦ ❛ ❛♣❧✐❝❛r ❡♠

  ❝❛❞❛ ❝❧❛ss❡ ❞❡ ❜♦♥✉s s❡r✐❛ ♦❜t✐❞♦ ♣♦r ❛♣❧✐❝❛çã♦ ❞♦ t❡♦r❡♠❛ ❛♥t❡r✐♦r ♣♦rt❛♥t♦✱ s❡r✐❛ E[E(S |λ)|Z = j], j = 1, . . . , s n ∆,n

  ✱ q✉❡ ❞❡♣❡♥❞❡ ❞❡ n✱ ♠❛s ❝♦♠♦ ❥á ❢♦✐ r❡❢❡r✐❞♦ ♥❛ ❙❡❝çã♦ ❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈ ✐♠♣❧í❝✐t❛ ♥♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s é ❤♦♠♦❣é♥❡❛✱ ♣♦rt❛♥t♦ ♦ ♣ré♠✐♦ é ✐♥❞❡♣❡♥❞❡♥t❡ ❞❡ n✱ ♦ q✉❡ é ❝♦♥tr❛❞✐tór✐♦✳

  ∆ (∆) < Q ( ˜ ∆) n n ❙❡❥❛♠ ❞♦✐s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s ∆ ❡ ˜ ✳ ❙❡ Q ✱ ♣❛r❛ t♦❞♦ n✱

  ∆ ❡♥tã♦ ♦❜✈✐❛♠❡♥t❡ q✉❡ ∆ é ♣r❡❢❡rí✈❡❧ ❛ ˜ ✳ ❉❛❞♦ q✉❡ ❡st❛ s✐t✉❛çã♦ ♥❡♠ s❡♠♣r❡ ❛❝♦♥t❡❝❡

  (∆) < Q ( ˜ ∆) (∆) > Q ( ˜ ∆) t❡♠✲s❡✱ ❡♠ ❣❡r❛❧✱ Q n n ♣❛r❛ ❛❧❣✉♥s ✈❛❧♦r❡s ❞❡ n ❡ Q n n ♣❛r❛ ♦✉tr♦s ✈❛❧♦r❡s ❞❡ n✳ ♣r♦♣õ❡ q✉❡ s❡ ♠✐♥✐♠✐③❡✱ ♣❛r❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛

  (∆) ❡s❝❛❧❛ ó♣t✐♠❛ ❞❡ ♣ré♠✐♦s✱ ♦ ✈❛❧♦r ❧✐♠✐t❡ ❞❡ Q n q✉❛♥❞♦ n t❡♥❞❡ ♣❛r❛ ✐♥✜♥✐t♦✱ ♦✉ s❡❥❛✱ 2

  [E(S|λ) − b(Z Q (∆) = E T )] n ✭✷✳✺✮

  ✷✳✶ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s ✶✼

  (∆) ❉❛❞♦ q✉❡ ♦ ♣ré♠✐♦ ❞❡ ❝r❡❞✐❜✐❧✐❞❛❞❡ é ❞❡t❡r♠✐♥❛❞♦ ♣❡❧❛ ♠✐♥✐♠✐③❛çã♦ ❞❡ Q ✱

  (∆) (j), j = 1, . . . , s T ❡♥tã♦ ❜❛st❛ ❞❡r✐✈❛r Q ❡♠ ♦r❞❡♠ ❛ b ❡✱ ✐❣✉❛❧❛♥❞♦ ❛ ③❡r♦✱ t❡r✲s❡✲á ❡♥tã♦ R ∞

  E(S|λ)π T (j)dU (λ) b (j) = , j = 1, . . . , s. T ✭✷✳✻✮ n π T (j)

  ◆♦t❡✲s❡ q✉❡✱ s❡ ❝♦♥s✐❞❡r❛r q✉❡ S ❞❡♣❡♥❞❡ ❛♣❡♥❛s ❞❡ λ ❛tr❛✈és ❞❛ ❞✐str✐❜✉✐çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s ❡ ❝♦♥s✐❞❡r❛r ♦ ✈❛❧♦r ❡s♣❡r❛❞♦ ❞❡ ❝❛❞❛ ✐♥❞❡♠♥✐③❛çã♦ ✉♠❛ ✉♥✐❞❛❞❡ ♠♦♥❡tár✐❛✱ t❡♠✲s❡ ❡♥tã♦ q✉❡ é ❡q✉✐✈❛❧❡♥t❡ ❛ R ∞

  λπ T (j)dU (λ) b (j) = . T ✭✷✳✼✮

  π (j) T ❊♥❝♦♥tr❛❞❛ ❛ ❡s❝❛❧❛ ♦♣t✐♠❛ ❞♦ s✐st❡♠❛✱ ❤á q✉❡ ❛✈❛❧✐❛r ❛ s✉❛ ❡✜❝✐ê♥❝✐❛✳

  ∆ T

  ❚❡♦r❡♠❛ ✷✳✷✳ ❙❡❥❛♠ ∆ ❡ ˜ ❞♦✐s s✐st❡♠❛s ❞❡ ❜♦♥✉s ❝♦♠ r❡❣r❛s ❞❡ tr❛♥s✐çã♦ T ❡ ˜ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❡ ❝♦♠ ❡s❝❛❧❛s ❞❡ ♣ré♠✐♦s ó♣t✐♠♦s ❝❛❧❝✉❧❛❞♦s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❢ór♠✉❧❛ T (∆) < Q ( ˜ ∆) T )

  T é ♠❛✐s ❡✜❝✐❡♥t❡ q✉❡ ˜ ♦✉ s❡❥❛ Q s❡ ❡ só s❡ e(T ) > e( ˜ ✱ ❝♦♠ 2 X s 2 e(T ) = E[b (Z T )] = b (j)π T (j). T T j=1 ✭✷✳✽✮ ❉❡♠♦♥str❛çã♦✳ P♦❞❡ s❡r ❝♦♥s✉❧t❛❞❛ ❡♠

  ❖ ✈❛❧♦r ❞❛ ❡✜❝✐ê♥❝✐❛ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s✱ só ♣♦r s✐ ♥ã♦ t❡♠ ♥❡♥❤✉♠ s✐❣♥✐✜❝❛❞♦✱ ❡st❡ ❝r✐tér✐♦ s❡r✈❡ ♣❛r❛ ❝♦♠♣❛r❛r ❛ ❡✜❝✐ê♥❝✐❛ ❞❡ ❞♦✐s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s ❞✐❢❡r❡♥t❡s✳

  ❊st❡ ♠♦❞❡❧♦ ♥ã♦ ❣❛r❛♥t❡ q✉❡✱ ❞❛❞♦ q✉❡ ❛s ❝❧❛ss❡s ❞❡ ❜♦♥✉s s❡❥❛♠ ♦r❞❡♥❛❞❛s ♣♦r ♦r❞❡♠ ❝r❡s❝❡♥t❡ ❞❡ ♣r♦♣❡♥sã♦ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✱ ❛ ❡s❝❛❧❛ ó♣t✐♠❛ ❞❡ ♣ré♠✐♦ ♦❜t✐❞❛ s❡❥❛ ❝r❡s❝❡♥t❡✳ ❖✉tr❛ ✐♥❝♦♥✈❡♥✐ê♥❝✐❛ ❞❡st❡ ♠♦❞❡❧♦✱ é ♦ ❢❛❝t♦ ❞❡ ❛♥❛❧✐s❛r ♦ ♣r♦❜❧❡♠❛ ❛ q✉❡ s❡ ♣r♦♣õ❡ r❡❝♦rr❡♥❞♦ ❡①❝❧✉s✐✈❛♠❡♥t❡ à ❞✐str✐❜✉✐çã♦ ❡st❛❝✐♦♥ár✐❛✱ ❡ ❝♦♠♦ s❡ s❛❜❡✱ ❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈ ♣♦❞❡ ❝♦♥✈❡r❣✐r ❧❡♥t❛♠❡♥t❡ ♣❛r❛ ❛ ❡st❛❝✐♦♥❛r✐❞❛❞❡✳

  ✷✳✶✳✷ ❖ ▼♦❞❡❧♦ ❞❡ ❇♦r❣❛♥✱ ❍♦❡♠ ✫ ◆♦r❜❡r❣

  ❖ ♠♦❞❡❧♦ ❛♣r❡s❡♥t❛❞♦ ♣♦r é ✉♠❛ ❣❡♥❡r❛❧✐③❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ♦♥❞❡ s❡ ❝♦♥s✐❞❡r❛ ❛ ✐♥tr♦❞✉çã♦ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ♣♦♥❞❡r❛❞♦r❡s {w ; n = 0, 1, . . .} n ✱ ♦♥❞❡ w n r❡♣r❡s❡♥t❛ ♦ ♣❡s♦ ❛ ❛tr✐❜✉✐r ❛♦ ♣❡rí♦❞♦ n ❡ w ♦ ♣❡s♦ ❛ ❛tr✐❜✉✐r à ❞✐str✐❜✉✐çã♦ ❡st❛❝✐♦♥ár✐❛✳ ❈♦♠♦ s❡r✐❛ ❞❡ ❡s♣❡r❛r✱ ❛ s♦♠❛ ❞❡ t♦❞♦s ♦s n = 0 = 1 ♣♦♥❞❡r❛❞♦r❡s é ✉♠✳ ◆♦t❛✲s❡ q✉❡✱ s❡ w ❡ w ♦❜té♠✲s❡ ♦ ♠♦❞❡❧♦ ❛♥t❡r✐♦r✳

  ❚❛❧ ❝♦♠♦ ♥♦ ♠♦❞❡❧♦ ❛♥t❡r✐♦r✱ ♣r❡t❡♥❞❡✲s❡ ♠✐♥✐♠✐③❛r ❛ ♣❡r❞❛ q✉❛❞rát✐❝❛ ❡s♣❡r❛❞❛✿ X ∞ ∞ s X Z ∞ X 2 (n) Q(∆) = w Q (∆) = w E(S |λ) − b(j) p (j)dU (λ) n n n n ∆,λ ✭✷✳✾✮

  ✶✽ ❈❛♣ít✉❧♦ ✷✳ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s ❡ ▼❡❞✐❞❛s ❞❡ ❆✈❛❧✐❛çã♦ ❞❡ ❙❇▼ (0) (j) = π T (j), j = 1, . . . , s

  ❝♦♠ p ∆,λ ✳ ❉❡r✐✈❛♥❞♦ Q(∆) ❡ ✐❣✉❛❧❛♥❞♦ ❛ ③❡r♦✱ ♦❜té♠✲s❡ q✉❡ ❛ ❡s❝❛❧❛ ❞❡ ♣ré♠✐♦s ó♣t✐♠♦s✿ P R ∞ ∞ (n) n=0 ∆,λ w E(S |λ)p (j)dU (λ) n n b (j) = B

  ✭✷✳✶✵✮ p ∆ (j) ♦♥❞❡ X Z ∞ (n) p ∆ (j) = w n p (j)dU (λ). n=0 ∆,λ ✭✷✳✶✶✮

  ❖ ❝r✐tér✐♦ ❞❡ ❡✜❝✐ê♥❝✐❛ ♣❛r❛ ❡st❡ ♠♦❞❡❧♦✱ s❡rá ❞❛❞♦ ♣♦r✿ X s 2 e(∆) = [b (j)] p (j) B ∆ j=1 ✭✷✳✶✷✮ ❖ t❡♦r❡♠❛ ❛♥t❡r✐♦r ♣♦❞❡ s❡r ❣❡♥❡r❛❧✐③❛❞♦ ✉s❛♥❞♦ ❡st❡ ❝r✐tér✐♦ ❞❡ ❡✜❝✐ê♥❝✐❛✳ ❚❛❧ ❝♦♠♦ ♦ ♠♦❞❡❧♦ ❛♥t❡r✐♦r✱ ❡st❡ t❛♠❜é♠ ♥ã♦ ❣❛r❛♥t❡ q✉❡✱ ❞❛❞♦ q✉❡ ❛s ❝❧❛ss❡s

  ❢♦r❛♠ ❞❡✜♥✐❞❛s ♣♦r ♦r❞❡♠ ❝r❡s❝❡♥t❡ ❞❡ ♣r♦♣❡♥sã♦ à s✐♥✐str❛❧✐❞❛❞❡✱ ❛ ❡s❝❛❧❛ ❞❡ ♣ré♠✐♦s ♦❜t✐❞♦s s❡❥❛ ❝r❡s❝❡♥t❡✳

  ✷✳✶✳✸ ❖ ▼♦❞❡❧♦ ❞❡ ●✐❧❞❡ ✫ ❙✉♥❞t

  ❖ ♠♦❞❡❧♦ ❛♣r❡s❡♥t❛❞♦ ♣♦r t❛♠❜é♠ ❞❡♥♦♠✐♥❛❞♦ ♣♦r ❊s❝❛❧❛ ▲✐✲ ♥❡❛r✱ ✈✐s❛ r❡s♦❧✈❡r ♦s ♣r♦❜❧❡♠❛s ❞♦s ♠♦❞❡❧♦s ❛♥t❡r✐♦r❡s✳ ❆ ❡s❝❛❧❛ ❞❡ ♣ré♠✐♦s é ❧✐♥✲ ❡❛r✐③❛❞❛ ❞❡ ❢♦r♠❛ ❛ q✉❡ ❡st❛ s❡❥❛ ❞❛❞❛ ♣♦r ♦r❞❡♠ ❝r❡s❝❡♥t❡ ❞❡ ❣r❛✈✐❞❛❞❡ ❞❡ s✐♥✐str❛❧✐✲ ❞❛❞❡✱ ❣❛r❛♥t✐♥❞♦ ❛ss✐♠ q✉❡ ❛s ✐rr❡❣✉❧❛r✐❞❛❞❡s ❞♦s ♠♦❞❡❧♦s ❛♥t❡r✐♦r❡s s❡❥❛♠ r❡s♦❧✈✐❞♦s ❡ ♦❜t❡♥❞♦✲s❡ ✉♠❛ ❡s❝❛❧❛ r❡❣✉❧❛r✳

  ❆ ❡s❝❛❧❛ ❞❡ ♣ré♠✐♦s ❧✐♥❡❛r✱ ♣r♦♣♦st❛ ♣♦r ❞❡ ♠♦❞♦ ❛ ♠✐♥✐♠✐③❛r é ❞❛❞❛ ♣♦r b(j) = a + jb , j = 1, . . . , s.

  ✭✷✳✶✸✮ ❉❛❞♦ q✉❡ s❡ ♣r❡t❡♥❞❡ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ❞❡ ♠✐♥✐♠✐③❛çã♦ ❞❡ ♥♦t❛✲s❡ q✉❡ X ∞ ∞ s X Z X 2 (n)

  Q (∆) = w Q (∆) = w [E(S |λ) − b(j)] p (j)dU (λ) = n n n n n X n=0 n=0 n=0 Z ∞ X s 2 (n) ∆,λ = w n E (S n |λ)p (j)dU (λ) + X n=0 ∞ s Z ∞ X j=1 2 (n) ∆,λ n=0 j=1 X ∞ s + w (b(j)) p (j)dU (λ) n Z ∞ X ∆,λ (n) − 2 w E(S |λ)b(j)p (j)dU (λ). n n ∆,λ

  ✷✳✶ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s ✶✾

  ❙✐♠♣❧✐✜❝❛♥❞♦ ❛ ❡①♣r❡ssã♦ ❛♥t❡r✐♦r✱ ♦❜té♠✲s❡✿ X ∞ s s Z 2 X 2 X Q(∆) = w E (S |λ)dU (λ) + (a + bj) p (j) − 2 (a + jb)b (j)p (j). n=0 j=1 j=1 n n ∆ B ∆ ✭✷✳✶✹✮

  ◆♦t❡✲s❡ q✉❡ ♦ ♣r✐♠❡✐r♦ t❡r♠♦ ❞♦ s❡❣✉♥❞♦ ♠❡♠❜r♦ é ✐♥❞❡♣❡♥❞❡♥t❡ ❞❛ ❡s❝❛❧❛ ❞❡ ♣ré♠✐♦s ❡s❝♦❧❤✐❞❛✱ ❡ ♦s r❡st❛♥t❡s t❡r♠♦s✱ q✉❛♥❞♦ s❡ ❡s❝♦❧❤❡ ❛ ❡s❝❛❧❛ ❞❡ ❇❛②❡s✱ ♦ s✐♠étr✐❝♦ ❛ e(∆)✱ ✜❝❛♥❞♦ ❛ss✐♠ ❣❡♥❡r❛❧✐③❛❞♦ ♦ ❚❡♦r❡♠❛

  ❖ ♣r♦❜❧❡♠❛ ❝❡♥tr❛❧ ❞♦ ♠♦❞❡❧♦ ♣r♦♣♦st♦ ♣♦r é ❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦s ♣❛râ♠❡tr♦s a ❡ b ❞❡ ♠♦❞♦ ❛ ♠✐♥✐♠✐③❛r Q(∆)✳ ❙❡♥❞♦ ❛ss✐♠✱ ❞❡r✐✈❛♥❞♦ ❛ ❡①♣r❡ssã♦ ❡♠ ♦r❞❡♠ ❛ a ❡ b ❡ ✐❣✉❛❧❛♥❞♦✲❛s ❛ ③❡r♦✱ t❡♠✲s❡ q✉❡ P P P s s s j=1 j=1 j=1 jb B (j)p ∆ (j) − jp ∆ (j) b B (j)p ∆ (j) b = L P P s s 2 2 j=1 j=1 j p (j) − ( jp (j)) ∆ ∆  s s P P ✭✷✳✶✺✮ a = b (j)p (j) − b jp (j) L B ∆ L ∆ j=1 j=1

  ❆ ❡s❝❛❧❛ ♦❜t✐❞❛ ♣❡❧♦ ♠♦❞❡❧♦ ❞❡ ✈❡♠ ❛ss✐♠✱ r❡s♦❧✈❡r ♦s ♣r♦❜❧❡✲ ♠❛s ❞❡ ♠♦♥♦t♦♥✐❛ ❡ ✐rr❡❣✉❧❛r✐❞❛❞❡s ❞♦s ♠♦❞❡❧♦s ❛♥t❡r✐♦r❡s✳ ◆♦ ❡♥t❛♥t♦✱ ♥❛❧❣✉♥s ❝❛s♦s r❛r♦s✱ ❛ ❡s❝❛❧❛ ❧✐♥❡❛r ♦❜t✐❞❛ ♥ã♦ é ❛❞♠✐ssí✈❡❧✱ ♣♦rq✉❡ ❛ ❡s❝❛❧❛ ❞❡ ♣ré♠✐♦s ♥❛s ❝❧❛ss❡s ❜♦♥✐✜❝❛❞❛s é ♥❡❣❛t✐✈❛✳

  ❆ ♠❡❞✐❞❛ ❞❡ ❡✜❝✐ê♥❝✐❛ ♣r♦♣♦st❛ ♣❡❧♦s ❛✉t♦r❡s ♣❛r❛ ♠❡❞✐r ❛ ♣❡r❞❛ ♦❝♦rr✐❞❛ ♣♦r s❡ ❡s❝♦❧❤❡r ❛ ❡s❝❛❧❛ ❧✐♥❡❛r ❡♠ ✈❡③ ❞❡ ❡s❝❛❧❛ ❞❡ ❇❛②❡s✱ é ❞❛❞❛ ♣❡❧♦ q✉♦❝✐❡♥t❡ ❡♥tr❡ ♦ ❡rr♦ q✉❛❞rát✐❝♦ ♠é❞✐♦ ❛ss♦❝✐❛❞♦ à ❡s❝❛❧❛ ❧✐♥❡❛r ❡ ♦ ❡rr♦ q✉❛❞rát✐❝♦ ♠é❞✐♦ ❛ss♦❝✐❛❞♦ à ❡s❝❛❧❛ ❞❡ ❇❛②❡s✳

  ✷✳✶✳✹ ❖ ▼♦❞❡❧♦ ❞❡ ❆♥❞r❛❞❡ ❡ ❙✐❧✈❛

  ❖ ♠♦❞❡❧♦ ❛♣r❡s❡♥t❛❞♦ ♣♦r t❛♠❜é♠ ❞❡♥♦♠✐♥❛❞♦ ♣♦r ❊s❝❛❧❛ ●❡♦♠étr✐❝❛✱ é ♦✉tr❛ ❛❧t❡r♥❛t✐✈❛ ♣❛r❛ s✉♣❡r❛r ❛s ❧❛❝✉♥❛s ❞♦ ♠♦❞❡❧♦ ❞❡ s♦❜ ❛ r❡str✐çã♦ ❞❡ q✉❡ j b(j) = a.b , j = 1, 2, . . . , s,

  ✭✷✳✶✻✮ ♦✉ s❡❥❛✱ ♣r❡t❡♥❞❡✲s❡ ❞❡t❡r♠✐♥❛r a ❡ b ❞❡ ♠♦❞♦ ❛ ♠✐♥✐♠✐③❛r X ∞ s s Z ∞ 2 j X 2 j X Q(∆) = w E (S |λ)dU (λ) + (a.b ) p (j) − 2 (a.b )b (j)p (j). n n ∆ B ∆ n=0 j=1 j=1 ✭✷✳✶✼✮

  P♦rt❛♥t♦✱ ❞❡r✐✈❛♥❞♦ ❡♠ ♦r❞❡♠ ❛ a ❡ b ❡ ✐❣✉❛❧❛♥❞♦ ❛ ③❡r♦✱ ♦❜té♠✲s❡✿ P s j j=1 b b (j)p (j) G B ∆ a = . G P ✭✷✳✶✽✮ s 2j

  ✷✵ ❈❛♣ít✉❧♦ ✷✳ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s ❡ ▼❡❞✐❞❛s ❞❡ ❆✈❛❧✐❛çã♦ ❞❡ ❙❇▼ ❡ " # X s s 2j−1 j−1 X a G a G jb p ∆ (j) − jb b B (j)p ∆ = 0 j=1 j=1 G G G ✭✷✳✶✾✮

  ❡①♣r❡ssã♦ ❡st❛ q✉❡ s❡ ♣♦❞❡ s✐♠♣❧✐✜❝❛r✱ s✉❜st✐t✉✐♥❞♦ ❛ ❡①♣r❡ssã♦ ❞❡ a ✱ ❡ t❡♥❞♦ ❡♠ G G ❝♦♥t❛ ♦s ✈❛❧♦r❡s ❛❞♠✐ssí✈❡✐s ♣❛r❛ a ❡ b ✱ ♦❜t❡♥❞♦✲s❡ ❛ s❡❣✉✐♥t❡ ❡q✉❛çã♦ X s s s s j 2j j 2j X X X j=1 j=1 j=1 j=1 b b (j) jb p (j) = jb b (j)p (j) b p (j). G G G G B ∆ B ∆ ∆ ✭✷✳✷✵✮ G

  ❊♠❜♦r❛ ♦ ❛✉t♦r ♥ã♦ ♣r♦✈❡ ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠❛ s♦❧✉çã♦ ú♥✐❝❛ ❞❡ b ♥❛ ❡q✉❛çã♦ ❡♠ t♦❞♦s ♦s ❡①❡♠♣❧♦s q✉❡ ❞❡t❡r♠✐♥♦✉ ❛ s♦❧✉çã♦ ♥✉♠ér✐❝❛ ❞❡st❛ ❡q✉❛çã♦✱ ♠♦str♦✉ G ❡①✐st✐r ✉♠❛ ❡ ✉♠❛ só s♦❧✉çã♦ ❛❞♠✐ssí✈❡❧ ♣❛r❛ b ✳ ❖ ♣♦♥t♦ ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡ q✉❡ s❡ ♦❜t✐✈❡r s❡rá ❝❡rt❛♠❡♥t❡ ✉♠ ♠✐♥✐♠✐③❛♥t❡✱ ❥á q✉❡ ∂Q(∆)/∂b < 0 ❡♠ b = 1 ❡ ♦s ✈❛✲ G > 1 ❧♦r❡s ❛❞♠✐ssí✈❡✐s s✉♣õ❡♠ b ✳ ❚❛❧ ❝♦♠♦ r❡❢❡r✐❞♦ ♣❡❧♦ ❛✉t♦r✱ ❛♣❡s❛r ❞❛s ❧❛❝✉♥❛s q✉❡ ♦ ♠♦❞❡❧♦ ♦r✐❣✐♥❛✱ é ✐♠♣♦rt❛♥t❡ r❡❢❡r✐r q✉❡✱ ❡♠ t❡r♠♦s ♣rát✐❝♦s✱ ❛s s♦❧✉çõ❡s ❛❞♠✐s✲

  

  sí✈❡✐s s✐t✉❛♠✲s❡ ♥✉♠ ✐♥t❡r✈❛❧♦ r❡❧❛t✐✈❛♠❡♥t❡ ♦ q✉❡ t♦r♥❛ ♣♦ssí✈❡❧ ✉♠ ❡st✉❞♦ ❝✉✐❞❛❞♦ ❞❡st❡ ✐♥t❡r✈❛❧♦ ♣♦r ❢♦r♠❛ ❛ ✈❡r✐✜❝❛r ❛ ✉♥✐❝✐❞❛❞❡ ❞❛ s♦❧✉çã♦✱ ❡♠ ❝❛❞❛ s✐t✉❛çã♦ ❝♦♥❝r❡t❛✳

  ❆ ♠❡❞✐❞❛ ❞❡ ❡✜❝✐ê♥❝✐❛ ❞❡st❛ ❡s❝❛❧❛ ♣❛r❛ ♠❡❞✐r ❛ ❡✜❝✐ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ é s❡♠❡❧❤❛♥t❡ à ❞❡✜♥✐❞❛ ♥❛ ❡s❝❛❧❛ ❧✐♥❡❛r✱ ♦✉ s❡❥❛✱ é ♦ q✉♦❝✐❡♥t❡ ❡♥tr❡ ♦ ❡rr♦ q✉❛❞rát✐❝♦ ♠é❞✐♦ ❛ss♦❝✐❛❞♦ à ❡s❝❛❧❛ ❣❡♦♠étr✐❝❛ ❡ ♦ ❡rr♦ q✉❛❞rát✐❝♦ ♠é❞✐♦ ❛ss♦❝✐❛❞♦ à ❡s❝❛❧❛ ❞❡ ❇❛②❡s✳

  ✷✳✷ ▼❡❞✐❞❛s ❞❡ ❆✈❛❧✐❛çã♦

  ♣r♦♣õ❡ ✈ár✐❛s ♠❡❞✐❞❛s ❞❡ ❛✈❛❧✐❛çã♦ ❡ ❝♦♠♣❛r❛çã♦ ❞❡ s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s✳ ❊st❛s ♠❡❞✐❞❛s ❞❡✈❡♠ s❡r ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❞❡ ❞✐❢❡r❡♥t❡s s✐st❡♠❛s ❡ ♥ã♦ ❛♣❡♥❛s ♣❛r❛ ❛✈❛❧✐❛r ✉♠ ú♥✐❝♦ s✐st❡♠❛✳

  ❖s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s ♣♦❞❡♠ s❡r ❛✈❛❧✐❛❞♦s s♦❜ ❛ ♣❡rs♣❡❝t✐✈❛ ❞❡ ✉♠ s❡❣✉r❛❞♦ ♦✉ s❡❣✉r❛❞♦r❛✳ ❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❡♠ ❛♠❜❛s ❛s ♣❡rs♣❡❝t✐✈❛s s❡rã♦ ♠✉✐t♦ ❞✐❢❡r❡♥t❡s✱ ✈✐st♦ q✉❡ ♥❡♠ s❡♠♣r❡ ♦s s❡❣✉r❛❞♦s ❞❡❝❧❛r❛♠ t♦❞♦s ♦s s✐♥✐str♦s✱ ♣♦rt❛♥t♦ ❛ ❞✐str✐❜✉✐çã♦ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♦❜s❡r✈❛❞❛ ❞♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s é ❞✐❢❡r❡♥t❡ ❡♠ ❛♠❜♦s ♦s ❝❛s♦s✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ♦ r❡s✉❧t❛❞♦ ❞❛s ♠❡❞✐❞❛s ❞❡ ❛✈❛❧✐❛çã♦ ❡♠ ❛♠❜❛s ❛s ♣❡rs♣❡❝t✐✈❛s ❞✐❢❡r❡♠✳

  ❆♦ ❧♦♥❣♦ ❞❡st❡ ❝❛♣ít✉❧♦ s❡rã♦ ❞❡s❝r✐t♦s ❛❧❣✉♠❛s ♠❡❞✐❞❛s ❞❡ ❛✈❛❧✐❛çã♦ ❞❡ s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s ♣r♦♣♦st❛s ♣♦r ♣❛r❛ ✉♠❛ ❞❛❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✱ s♦❜ ❛ ♣❡rs♣❡❝t✐✈❛ ❞❛ s❡❣✉r❛❞♦r❛✳ b G

  ❞❡✈❡ s✐t✉❛r✲s❡ ❡♥tr❡ ✶ ❡ ✉♠ ✈❛❧♦r q✉❡✱ ❡♠❜♦r❛ ❞❡♣❡♥❞❡♥t❡ ❞♦ ♥ú♠❡r♦ ❞❡ ❝❧❛ss❡s ❞♦ s✐st❡♠❛ ❡ ❞❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦✱ t❡rá ❝❡rt❛♠❡♥t❡ ✉♠ ♠á①✐♠♦ ❛❜s♦❧✉t♦ ✐♥❢❡r✐♦r ❛ ✸✳

  ✷✳✷ ▼❡❞✐❞❛s ❞❡ ❆✈❛❧✐❛çã♦ ✷✶

  ✷✳✷✳✶ ❖ ◆í✈❡❧ ▼é❞✐♦ ❘❡❧❛t✐✈♦ ❞❡ ❊st❛❝✐♦♥❛r✐❞❛❞❡

  ❖ ♥í✈❡❧ ♠é❞✐♦ r❡❧❛t✐✈♦ ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡ ❞❡s✐❣♥❛❞♦ ♣♦r RS ♠❡❞❡ ♦ ♥í✈❡❧ ❞❡ ❛❣❧♦✲ ♠❡r❛çã♦ ❞❛s ❛♣ó❧✐❝❡s ♥♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s✱ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✳ ❖ ✈❛❧♦r ❞❡ RSAL ❡♥❝♦♥tr❛✲s❡ ❡♥tr❡ ✵ ❡ ✶✳ ❯♠ ✈❛❧♦r ❜❛✐①♦ ❞❡ RSAL ✐♥❞✐❝❛ q✉❡ ❡①✐st❡ ✉♠❛ ❣r❛♥❞❡ ❛❣❧♦♠❡r❛çã♦ ❞❡ ❛♣ó❧✐❝❡s ♥❛s ❝❧❛ss❡s ♠❛✐s ❜❛✐①❛s ❞♦ s✐st❡♠❛ ❡♥q✉❛♥t♦ q✉❡✱ ✉♠ ✈❛❧♦r ❛❧t♦ ✐♥❞✐❝❛ ✉♠❛ ♠❡❧❤♦r ❞✐str✐❜✉✐çã♦ ❞❛s ❛♣ó❧✐❝❡s ♥♦ s✐st❡♠❛✳ ❖ ✈❛❧♦r ✐❞❡❛❧ ♣❛r❛ RSAL s❡r✐❛ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✵✳✺ ♠❛s✱ ♥♦ ❡♥t❛♥t♦✱ ❞✐✜❝✐❧♠❡♥t❡ ✉♠ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❛t✐♥❣❡ ❡ss❡ ✈❛❧♦r✳

  ❖ ♥í✈❡❧ ♠é❞✐♦ r❡❧❛t✐✈♦ ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ♣❛r❛ ✉♠❛ ❞❛❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐✲ ❞❛❞❡ λ s❡rá ❞❛❞♦ ♣♦r✿

  P M (Z ) − λ T Pré♠✐♦ ▼á①✐♠♦

  RSAL λ = ✭✷✳✷✶✮

  Pré♠✐♦ ▼á①✐♠♦ − Pré♠✐♦ ▼í♥✐♠♦ ♦♥❞❡ X s

  P M (Z ) = b(j)π (j) λ T T,λ j=1 ✭✷✳✷✷✮ é ♦ ♣ré♠✐♦ ♠é❞✐♦ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡ ♣❛r❛ ✉♠❛ ❞❛❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐s✲ tr❛❧✐❞❛❞❡ λ✳

  ❖ ♥í✈❡❧ ♠é❞✐♦ r❡❧❛t✐✈♦ ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡ ♣❛r❛ ✉♠❛ ❛♣ó❧✐❝❡ r❡t✐r❛❞❛ ❛♦ ❛❝❛s♦ ❞❡ ✉♠❛ ❝❛rt❡✐r❛ ❞❡ ❛♣ó❧✐❝❡s✱ ♦✉ s❡❥❛✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ❞✐str✐❜✉✐çã♦ ❡str✉t✉r❛✱ é ❞❛❞❛ ♣♦r✿

  P M (Z ) − T Pré♠✐♦ ▼í♥✐♠♦

  RSAL = ✭✷✳✷✸✮

  Pré♠✐♦ ▼á①✐♠♦ − Pré♠✐♦ ▼í♥✐♠♦ ♦♥❞❡ X s

  P M (Z ) = b(j)π (j) T T ✭✷✳✷✹✮ j=1 é ♦ ♣ré♠✐♦ ♠é❞✐♦ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✳

  ❚❡♠ q✉❡ s❡ t❡r ❛t❡♥çã♦ ❛♦ t✐r❛r ❝♦♥❝❧✉sõ❡s ❞♦ r❡s✉❧t❛❞♦ ♦❜t✐❞♦ ✉t✐❧✐③❛♥❞♦ ❡st❡ ❝r✐tér✐♦✱ ✈✐st♦ q✉❡ ♦s r❡s✉❧t❛❞♦s sã♦ ❡♠ ❢✉♥çã♦ ❞♦ ♣ré♠✐♦ ♠á①✐♠♦ ❡ ❝♦♠♦ s❡ s❛❜❡✱ ♣♦✉❝❛s ❛♣ó❧✐❝❡s s❡ ❡♥❝♦♥tr❛♠ ♥❛ ❝❧❛ss❡ ♠❛✐s ❛❣r❛✈❛❞❛ ❞♦ s✐st❡♠❛✳

  ✷✳✷✳✷ ❈♦❡✜❝✐❡♥t❡ ❞❡ ❱❛r✐❛çã♦ ❞❡ Pré♠✐♦s

  ◆❛ t❛r✐❢❛çã♦ ❛ ♣r✐♦r✐✱ ❛ss✉♠❡✲s❡ q✉❡ ♦ r✐s❝♦ ❞❡ ♦❝♦rrê♥❝✐❛ ❞❡ ✉♠ s✐♥✐str♦ é ❛❧❡❛tór✐♦ ❡ ♦s r✐s❝♦s sã♦ ❛❣r✉♣❛❞♦s ❡♠ ❝❧❛ss❡s ♠❛✐s ♦✉ ♠❡♥♦s ❤♦♠♦❣é♥❡❛s✱ ❞❡ ♠♦❞♦ ❛ q✉❡ s❡❣✉r❛❞♦s ❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s s❡♠❡❧❤❛♥t❡s ♣❛❣✉❡♠ ♦ ♠❡s♠♦ ♣ré♠✐♦✳ ❖ ♣ré♠✐♦ é✱ ❛ss✐♠✱ ✉♠❛ ✈❛r✐á✈❡❧ ✜①❛ ❡ ♣♦rt❛♥t♦ ❛ tr❛♥s❢❡rê♥❝✐❛ ❞♦ r✐s❝♦ ❞♦ s❡❣✉r❛❞♦ ♣❛r❛ ❛ s❡❣✉r❛❞♦r❛ é t♦t❛❧✱ ❧❡✈❛♥❞♦ ❛ ✉♠❛ ✈❛r✐❛çã♦ ❞❡ ♣ré♠✐♦s ♥✉❧❛✳

  ❖ r✐s❝♦ ❞❡ ♦❝♦rrê♥❝✐❛ ❞❡ ✉♠ s✐♥✐str♦ ✈❛r✐❛ ❞❡ s❡❣✉r❛❞♦ ♣❛r❛ s❡❣✉r❛❞♦ ❡ ❛♥♦ ❛♣ós ❛♥♦✳ ❖ ♣ré♠✐♦ é ♦ r❡s✉❧t❛❞♦ ❞♦s s✐♥✐str♦s ❞❡❝❧❛r❛❞♦s ❡ é ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ♣♦rt❛♥t♦✱ ❛

  ❘❡❧❛t✐✈❡ ❙t❛t✐♦♥❛r② ❆✈❡r❛❣❡ ▲❡✈❡❧✳

  ✷✷ ❈❛♣ít✉❧♦ ✷✳ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s ❡ ▼❡❞✐❞❛s ❞❡ ❆✈❛❧✐❛çã♦ ❞❡ ❙❇▼ s✉❛ ✈❛r✐❛❜✐❧✐❞❛❞❡ ♥ã♦ é ♥✉❧❛✳ P♦❞❡✲s❡ ♣r♦✈❛r ✭✈❡r q✉❡ ✉♠ s❡❣✉r❛❞♦✱ s❡♠ ✉♠ ❝♦♥tr❛t♦ ❞❡ s❡❣✉r♦✱ ❡stá ❡①♣♦st♦ ❛ ✉♠ ♣r♦❝❡ss♦ ❞❡ ♣❡r❞❛ ❝♦♠ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✈❛r✐❛çã♦ ❞❡ ✻✱✹✳ ❉❛❞♦ q✉❡ ♥❛ ❛✉sê♥❝✐❛ ❞❛ t❛r✐❢❛çã♦ ❛ ♣♦st❡r✐♦r✐ ♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✈❛r✐❛çã♦ é ♥✉❧♦✱ ♣♦❞❡ ❝♦♥✲ ❝❧✉✐r✲s❡ ❡♥tã♦ q✉❡✱ ❝♦♠ ❛ t❛r✐❢❛çã♦ ❛ ♣♦st❡r✐♦r✐ ♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✈❛r✐❛çã♦ ✈❛r✐❛ ❡♥tr❡ ✵ ❡ ✻✱✹✳

  ❖ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✈❛r✐❛çã♦ ❞♦s ♣ré♠✐♦s ✭❞❡s✐❣♥❛❞♦ ♣♦r CV ✮ é ❞❡✜♥✐❞♦ ❝♦♠♦ ♦ q✉♦✲ ❝✐❡♥t❡ ❞♦s ❞❡s✈✐♦s ♣❛❞rõ❡s ❞♦s ♣ré♠✐♦s ❡ ♦ ♣ré♠✐♦ ♠é❞✐♦✱ ❛♠❜♦s ❝❛❧❝✉❧❛❞♦s ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✳

  ❖ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✈❛r✐❛çã♦ ❞♦s ♣ré♠✐♦s✱ ♣❛r❛ ✉♠❛ ❞❛❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ λ

  ✱ é ❞❛❞♦ ♣♦r✿ h i P s 2 2 1/2 j=1 b (j)π (j) − P M (Z ) T,λ ∆ λ CV = . λ ✭✷✳✷✺✮

  P M (Z ) λ ∆ ❖ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✈❛r✐❛çã♦ ❞❡ ♣ré♠✐♦s✱ ♣❛r❛ ✉♠❛ ❛♣ó❧✐❝❡ r❡t✐r❛❞❛ ❛♦ ❛❝❛s♦✱ ♦✉ s❡❥❛✱

  ❝♦♥s✐❞❡r❛♥❞♦ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❡str✉t✉r❛✱ é ❞❛❞♦ ♣♦r✿ P s 2 2 1/2 j=1 b (j)π (j) − P M (Z ) T ∆ CV = .

  ✭✷✳✷✻✮ P M (Z )

  ✷✳✷✳✸ ❆ ❊❧❛st✐❝✐❞❛❞❡ ❞♦ Pré♠✐♦ ▼é❞✐♦

  ❯♠ ❞♦s ♦❜❥❡❝t✐✈♦s ❞❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s é ❣❛r❛♥t✐r q✉❡ ♦s ✏❜♦♥s✑ s❡❣✉r❛❞♦s ✭❛q✉❡❧❡s q✉❡ ♥ã♦ ❞❡❝❧❛r❛♠ s✐♥✐str♦s✮ ♣❛❣✉❡♠ ✉♠ ♣ré♠✐♦ ❜❛✐①♦ ❡ q✉❡ ♦s ✏♠❛✉s✑ s❡❣✉r❛❞♦s ♣❛❣✉❡♠ ♣ré♠✐♦s ❡❧❡✈❛❞♦s✱ ❝♦♥tr✐❜✉✐♥❞♦ ❛ss✐♠✱ ♣❛r❛ ✉♠❛ ❝♦♥❞✉çã♦ ♠❛✐s ❝❛✉t❡❧♦s❛✳ ❙❡♥❞♦ ❛ss✐♠✱ ♦ s✐st❡♠❛ t❡♠ q✉❡ r❡s♣♦♥❞❡r ❛ ❛❧t❡r❛çõ❡s ❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ ❞❡ ♠♦❞♦ ❛ ❣❛r❛♥t✐r ✉♠❛ t❛r✐❢❛çã♦ ❥✉st❛✳

  ❆ ❡❧❛st✐❝✐❞❛❞❡ ❞♦ ♣ré♠✐♦ ♠é❞✐♦✱ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ♠❡❞❡ ❛ r❡s♣♦st❛ ❞♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❞❛❞♦ q✉❡ ♦❝♦rr❡✉ ✉♠❛ ❛❧t❡r❛çã♦ ♥❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐✲ ❞❛❞❡✳ ❊st❡ ❝♦♥❝❡✐t♦ ❢♦✐ ♣r✐♠❡✐r♦ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ❡ ♣♦st❡r✐♦r♠❡♥t❡ ♣♦r

  ◆✉♠ s✐st❡♠❛ ❞❡ ❜♦♥✉s r❛③♦á✈❡❧✱ ♦ ♣ré♠✐♦ ❞❡ ❝❛❞❛ s❡❣✉r❛❞♦ ❞❡♣❡♥❞❡ ❞❛ s✉❛ ❢r❡q✉ê♥✲ ❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ λ ❡ ✐❞❡❛❧♠❡♥t❡ ❡ss❛ ❞❡♣❡♥❞ê♥❝✐❛ ❞❡✈✐❛ s❡r ❧✐♥❡❛r✳ ❯♠ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❞✐③✲s❡ ♣❡r❢❡✐t❛♠❡♥t❡ ❡❧ást✐❝♦ s❡✱ ❞❛❞♦ q✉❡ ♦❝♦rr❡✉ ✉♠ ❛✉♠❡♥t♦ r❡❧❛t✐✈♦ ♥❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✱ ♦❝♦rr❡ ♦ ♠❡s♠♦ ❛✉♠❡♥t♦ r❡❧❛t✐✈♦ ♥♦ ♣ré♠✐♦ ❞♦ s❡❣✉r❛❞♦✳

  ❆ ❡❧❛st✐❝✐❞❛❞❡ ❞♦ s✐st❡♠❛✱ ♣❛r❛ ✉♠❛ ❞❛❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ λ s❡rá ❞❛❞❛ ♣♦r dP M (Z )/P M (Z ) d ln P M (Z ) λ T λ T λ T

  η(λ) = = ✭✷✳✷✼✮ dλ/λ d ln λ

  (Z ) ♦♥❞❡ P M é ♦ ♣ré♠✐♦ ♠é❞✐♦ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ❞❛❞❛ ❛ ❢r❡q✉ê♥❝✐❛

  • η(λ) < 0
  • 0 < η(λ) < 1
  • η(λ) > 1 t❡r✲s❡✲✐❛ q✉❡ ♦ ❛✉♠❡♥t♦ ❞♦s ♣ré♠✐♦s é s✉♣❡r✐♦r ❛♦ ❛✉♠❡♥t♦ ❞❛ ❢r❡q✉ê♥✲
  • η(λ) = 1

  q✉❡ é ✜♥✐t♦✱ ♣♦rt❛♥t♦✿ d ln P M λ (Z ) d ln λ

  = dπ T ,λ dλ

   dπ T ,λ dλ

  q✉❡ ♦ ❝á❧❝✉❧♦ ❞❛ ❡❧❛st✐❝✐❞❛❞❡ é ♦❜t✐❞❛ ❛tr❛✈és dP M (Z ) dλ = s X j=1 dπ T (j) dλ b(j). ❘❡❝♦rr❡♥❞♦ ❛♦ s✐st❡♠❛ ❞❡ ❡q✉❛çõ❡s✿

  ✭✷✳✷✽✮ ❈❛s♦ s❡ ♦♣t❡ ♣❡❧❛ ❞✐s❝r❡t✐③❛çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❡str✉t✉r❛❧✱ ❤á q✉❡ t❡r ❡♠ ❝♦♥t❛✱ ✈❡r

  ❞♦ ✈❛❧♦r ❞♦ ❡s♣❡r❛❞♦ ❞❛ ❡❧❛st✐❝✐❞❛❞❡✱ ❞❛❞❛ ❛ ❞✐str✐❜✉✐çã♦ ❡str✉t✉r❛❧✱ ♦✉ s❡❥❛✿ η = Z η(λ)dU (λ).

  ♣♦s✐t✐✈♦✱ ❡ ✈♦❧t❛ ❛ ❛♣r♦①✐♠❛r✲s❡ ♥♦✈❛♠❡♥t❡ ❞❡ ③❡r♦✱ q✉❛♥❞♦ λ t❡♥❞❡ ♣❛r❛ ✐♥✜♥✐t♦✳ ✐♥tr♦❞✉③✐✉ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❣❧♦❜❛❧✱ q✉❡ é ♦❜t✐❞❛ ❛tr❛✈és

  = 0. ❈♦♥❝❧✉✐✲s❡ ❡♥tã♦ q✉❡ ❛ ❡❧❛st✐❝✐❞❛❞❡ ♣❛rt❡ ❞❡ ③❡r♦✱ ❞❡s❝r❡✈❡ ✉♠❛ ❝✉r✈❛ ♥♦ q✉❛❞r❛♥t❡

  ✱ ♣♦rt❛♥t♦ ♥ã♦ é ♣❡r❢❡✐t❛♠❡♥t❡ ❡❧ást✐❝❛✱ ❞❛❞♦ q✉❡✿

  ➱ ♣♦ssí✈❡❧ ❞❡♠♦♥str❛r q✉❡ ❛ ❡❧❛st✐❝✐❞❛❞❡ ♥ã♦ ❛t✐♥❣❡ ♦ ✈❛❧♦r ✶ ♣❛r❛ t♦❞♦ ♦ ✈❛❧♦r ❞❡ λ

  é ❛ s✐t✉❛çã♦ ♦♥❞❡ ♦ s✐st❡♠❛ é ❝♦♥s✐❞❡r❛❞♦ ♣❡r❢❡✐t❛♠❡♥t❡ ❡❧ást✐❝♦✳ ❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❝♦♠❡r❝✐❛❧ t❛♠❜é♠ ♥ã♦ é ❛❝♦♥s❡❧❤❛❞♦ ♣♦✐s é ♣♦✉❝♦ ❝♦♠♣❡t✐t✐✈♦✳

  ❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✳ ❊st❛ s✐t✉❛çã♦ ♥ã♦ é ❛❝♦♥s❡❧❤á✈❡❧ ✈✐st♦ q✉❡ ♣r♦✈♦❝❛r✐❛ ♦ ❛❜❛♥❞♦♥♦ ❞❡ s❡❣✉r❛❞♦s ♣♦✐s s❡r✲❧❤❡s✲✐❛ ❞❡s❢❛✈♦rá✈❡❧❀

  é ♦ ❝❛s♦ ♠❛✐s ❤❛❜✐t✉❛❧✱ ♦♥❞❡ ♦s ❛✉♠❡♥t♦s ♥♦s ♣ré♠✐♦s sã♦ ✐♥❢❡r✐♦r❡s ❛♦s ❛✉♠❡♥t♦s ♥❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡❀

  ♥ã♦ ❢❛③ s❡♥t✐❞♦✱ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ♣rát✐❝♦✱ ✈✐st♦ q✉❡✱ ❝♦♠ ✉♠ ❛✉♠❡♥t♦ ♥❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ t❡r✲s❡✲✐❛ ✉♠❛ ❞✐♠✐♥✉✐çã♦ ♥♦ ♣ré♠✐♦❀

  ❖s ✈❛❧♦r❡s ♣♦ssí✈❡✐s ❞❡ η(λ) ♣♦❞❡♠ s❡r ✐♥t❡r♣r❡t❛❞♦s ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿

  ✷✳✷ ▼❡❞✐❞❛s ❞❡ ❆✈❛❧✐❛çã♦ ✷✸

  • η(0) = 0
  • ◗✉❛♥❞♦ λ t❡♥❞❡ ♣❛r❛ ✐♥✜♥✐t♦ ♦ ♣ré♠✐♦ ♠é❞✐♦ t❡♥❞❡ ♣❛r❛ max b(i) i=1,...,s

  P T

  • π T dP T ,λ dλ s
  • X dπ T (j) dλ = 0

      ✷✹ ❈❛♣ít✉❧♦ ✷✳ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s ❡ ▼❡❞✐❞❛s ❞❡ ❆✈❛❧✐❛çã♦ ❞❡ ❙❇▼ ♦✉ s❡❥❛✱ dπ T (j) 1

      = π B (I − A ) , T ,λ T ,λ T ,λ T dλ ♦♥❞❡ A é ✉♠❛ ♠❛tr✐③ ❝✉❥❛s s − 1 ♣r✐♠❡✐r❛s ❝♦❧✉♥❛s ❝♦rr❡s♣♦♥❞❡♠ às ❝♦❧✉♥❛s ❞❛ T ,λ ♠❛tr✐③ P ❡ ❛ ú❧t✐♠❛ ❝♦❧✉♥❛ t♦♠❛ ♦ ✈❛❧♦r ✲✶✱ à ❡①❝❡♣çã♦ ❞♦ ú❧t✐♠♦ q✉❡ t♦♠❛ ✈❛❧♦r ✵ T T /dλ

      ❡ B é ✉♠❛ ♠❛tr✐③ ❝✉❥❛s ❝♦❧✉♥❛s sã♦ ❛s ❞❛ ♠❛tr✐③ dP ✱ à ❡①❝❡♣çã♦ ❞❛ ú❧t✐♠❛ ❝♦❧✉♥❛✱ ❝✉❥♦s ❡❧❡♠❡♥t♦s t♦♠❛♠ ✈❛❧♦r ✵✳

      ✷✳✷✳✹ ❆ ❊❧❛st✐❝✐❞❛❞❡ ❚r❛♥s✐❡♥t❡

      ❖✉tr♦ ❝♦♥❝❡✐t♦ ❞❡ ❡❧❛st✐❝✐❞❛❞❡ é ✐♥tr♦❞✉③✐❞♦ ♣♦r ❞❡s✐❣♥❛❞♦ ♣♦r ❡❧❛s✲ t✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡✱ ♦♥❞❡ ♦ ❛✉t♦r ❛❜♦r❞❛ ♦ ♣r♦❜❧❡♠❛ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❡❝♦♥ó♠✐❝♦✱ λ (j) ✐♥tr♦❞✉③✐♥❞♦ ✉♠❛ t❛①❛ ❞❡ ❞❡s❝♦♥t♦ 0 < β < 1✱ ❛ ♣❛rt✐r ❞♦ q✉❛❧ s❡ ❝❛❧❝✉❧❛ V ✱ ♦ ✈❛❧♦r ❡s♣❡r❛❞♦ ❛❝t✉❛❧✐③❛❞♦ ❛ ♣❛❣❛r ❡♠ ❤♦r✐③♦♥t❡ ✐♥✜♥✐t♦✱ ♣♦r ✉♠❛ ❛♣ó❧✐❝❡ q✉❡ s❡ ❡♥✲ j ❝♦♥tr❛ ♥❛ ❝❧❛ss❡ C ✱ ♥♦ ♣r❡s❡♥t❡ ♣❡rí♦❞♦✱ ♣❛r❛ ✉♠❛ ❞❛❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ λ

      ✱ ❛tr❛✈és ❞❡✿ X s P V λ (j) = b(j) + β T ,λ (j, l)V λ (l) , j = 1, . . . , s. l=1

      ✭✷✳✷✾✮ ❘❡❝♦rr❡♥❞♦ ❛♦ ♣r✐♥❝í♣✐♦ ❞❛ ❝♦♥tr❛❝çã♦✱ ♣r♦✈❛ q✉❡ ♦ s✐st❡♠❛ ❞❡

      ❡q✉❛çõ❡s t❡♠ ✉♠❛ ú♥✐❝❛ s♦❧✉çã♦✳ ❆ ❡❧❛st✐❝✐❞❛❞❡ ❞♦ ✈❛❧♦r ❡s♣❡r❛❞♦ ❛❝t✉❛❧✐③❛❞♦ ❞♦s ♣❛❣❛♠❡♥t♦s ❢✉t✉r♦s ❡♠ r❡❧❛çã♦ à ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✱ ♣❛r❛ ✉♠❛ ❛♣ó❧✐❝❡ q✉❡ s❡ j ❡♥❝♦♥tr❛ ♥❛ ❝❧❛ss❡ C ✱ é✿ dV λ (j) V λ (j) µ (j) = . λ λ ✭✷✳✸✵✮

      ❈♦♥s✐❞❡r❛♥❞♦ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❡str✉t✉r❛✱ ❛ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡ ❞♦ s✐st❡♠❛ r❡❧✲ j ❛t✐✈❛ ❛ ✉♠ s❡❣✉r❛❞♦ q✉❡ s❡ s✐t✉❛ ♥❛ ❝❧❛ss❡ C ✱ é✿ Z ∞ µ(j) = µ λ (j)dU (λ).

      ✭✷✳✸✶✮

      ❈❛♣ít✉❧♦ ✸ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛

      ❆♦ ❧♦♥❣♦ ❞❡st❡ ❝❛♣ít✉❧♦ s❡rã♦ ❛♣❧✐❝❛❞♦s ♦s ♠ét♦❞♦s ❡ ♠♦❞❡❧♦s ❛♣r❡s❡♥t❛❞♦s ♥♦s ❝❛♣ít✉✲ ❧♦s ❛♥t❡r✐♦r❡s ✉s❛♥❞♦✱ ♣❛r❛ t❛❧✱ ♦s ❞❛❞♦s r❡❛✐s r❡❧❛t✐✈♦s à ❝❛rt❡✐r❛ ❞❡ ❛♣ó❧✐❝❡s ❞♦ s❡❣✉r♦ ❞❡ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❝✐✈✐❧ ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛✳ P❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦s r❡s✉❧t❛❞♦s s❡rá ✉t✐❧✐③❛❞♦ ♦ s♦❢t✇❛r❡ ▼❛t❤❡♠❛t✐❝❛ ✻✳✵ ❞❛ ❲♦❧❢r❛♠✳ ❈♦♠ ❜❛s❡ ♥❛s ❛♥á❧✐s❡s ❡ r❡s✉❧t❛❞♦s ♦❜t✐❞♦s✱ s❡rã♦ ❢❡✐t♦s ♦s r❡s♣❡❝t✐✈♦s ❝♦♠❡♥tár✐♦s ❡ ❝♦♥❝❧✉sõ❡s✳

      ❉❛❞♦ q✉❡ ♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s q✉❡ ✈✐❣♦r❛ ❛❝t✉❛❧♠❡♥t❡ ❡♠ ❈❛❜♦ ❱❡r❞❡ ❛♣r❡✲ s❡♥t❛ ❛❧❣✉♠❛s ❧❛❝✉♥❛s✱ ❝♦♠♦ s❡ ♣♦❞❡ ✈❡r✐✜❝❛r ♥❛ ❙✉❜✲❙❡❝çã♦ ♣r♦❝❡❞❡✉✲s❡ ❡♥tã♦ à ❛✈❛❧✐❛çã♦ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ♣r♦♣♦st♦ ♣♦r ❡ à ❛♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❡♥tr❡ ♦s ❞♦✐s s✐st❡♠❛s✳

      ✸✳✶ ◆ú♠❡r♦ ❞❡ ❙✐♥✐str♦s

      ◆♦ SBM q✉❡ ✈✐❣♦r❛ ❡♠ ❈❛❜♦ ❱❡r❞❡✱ ❜❡♠ ❝♦♠♦ ♥❛ ❣❡♥❡r❛❧✐❞❛❞❡ ❞♦s ♣❛ís❡s ❡ s❡❣✉✲ r❛❞♦r❛s✱ ❛ t❛r✐❢❛çã♦ ❛ ♣♦st❡r✐♦r✐ é ❢❡✐t❛ ❡①❝❧✉s✐✈❛♠❡♥t❡ ❝♦♠ ❜❛s❡ ♥♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s ❞❡❝❧❛r❛❞♦s✳ P♦❞❡r✲s❡✲á ❛ss✐♠ ❝♦♥s✐❞❡r❛r ♦ ♠♦♥t❛♥t❡ ❡s♣❡r❛❞♦ ❛ss♦❝✐❛❞♦ ❛ ❝❛❞❛ s✐♥✐str♦ ❝♦♠♦ s❡♥❞♦ ✉♥✐tár✐♦ ❡✱ ♣♦rt❛♥t♦✱ ♦ ♣ré♠✐♦ ♣✉r♦ ❞❡ ❝❛❞❛ s❡❣✉r❛❞♦✱ s❡rá ❞❛❞♦ ♣❡❧❛ s✉❛ ♣ró♣r✐❛ ❢r❡q✉ê♥❝✐❛ ❡s♣❡r❛❞❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✳

      ❆♦ ❧♦♥❣♦ ❞❡st❛ s❡❝çã♦ s❡rã♦ ❞❡s❝r✐t♦s ❛❧❣✉♥s ♠♦❞❡❧♦s q✉❡ ♣❡r♠✐t❡♠ ❛❥✉st❛r ✉♠❛ ❞✐str✐❜✉✐çã♦ ❛♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s q✉❡ ✉♠ s❡❣✉r❛❞♦ ♣♦❞❡ ❞❡❝❧❛r❛r à s❡❣✉r❛❞♦r❛ ♥✉♠❛ ❛♥✉✐❞❛❞❡✱ ♦✉ s❡❥❛✱ ✉♠❛ ❞✐str✐❜✉✐çã♦ q✉❡ s❡❥❛ s✐❣♥✐✜❝❛t✐✈❛ ♣❛r❛ r❡♣r❡s❡♥t❛r ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ ❛♥✉❛❧✳

      

    ✸✳✶✳✶ Pr♦❝❡ss♦ ❞❡ P♦✐ss♦♥ ❍♦♠♦❣é♥❡♦ ✲ ❈❛rt❡✐r❛ ❍♦♠♦❣é♥❡❛

      ◆❡st❡ ♠♦❞❡❧♦✱ ❝♦♥s✐❞❡r❛✲s❡ q✉❡ ♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s ❞❡❝❧❛r❛❞♦s s❡❣✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ P♦✐ss♦♥ ❞❡ ♣❛râ♠❡tr♦ ❝♦♥st❛♥t❡✱ λ✱ ✐st♦ é✱ ❝♦♥s✐❞❡r❛✲s❡ q✉❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦s s❡❣✉r❛❞♦s ❞❡♥tr♦ ❞❡ ❝❛❞❛ ❝❧❛ss❡ ❞❡ r✐s❝♦ é ❤♦♠♦❣é♥❡♦✱ ♣❡❧♦ q✉❡✱ ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ✉♠ s✐✲

      ✷✻ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ s❡rá ❞❡s♥❡❝❡ssár✐❛ ✈✐st♦ ♥ã♦ ❡①✐st✐r ❤❡t❡r♦❣❡♥❡✐❞❛❞❡ ♥♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦s s❡❣✉r❛❞♦s ❞❡♥tr♦ ❞❡ ❝❛❞❛ ❝❧❛ss❡ ❞❡ r✐s❝♦✳ ❉❡✜♥✐çã♦ ✸✳✶✳ ❙❡❥❛ N(t) ♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s r❡❧❛t✐✈♦s ❛ ✉♠ ❞❡t❡r♠✐♥❛❞♦ r✐s❝♦✱ ♦❝♦rr✐❞♦s ♥♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ] 0 , t ] ❝♦♠ t > 0 ❡ N(0) = 0✳ ❉✐③✲s❡ q✉❡ {N(t)} t≥0 é ✉♠ ♣r♦❝❡ss♦ ❞❡ P♦✐ss♦♥ ❤♦♠♦❣é♥❡♦ ❞❡ ✐♥t❡♥s✐❞❛❞❡ λ✱ s❡ ✈❡r✐✜❝❛r ❛s s❡❣✉✐♥t❡s ❝♦♥❞✐çõ❡s✿

      ✶✳ ❖ ♣r♦❝❡ss♦ t❡♠ ✐♥❝r❡♠❡♥t♦s ✐♥❞❡♣❡♥❞❡♥t❡s❀ ✷✳ ❖ ♣r♦❝❡ss♦ t❡♠ ✐♥❝r❡♠❡♥t♦s ❡st❛❝✐♦♥ár✐♦s❀

      

      ✸✳ P❛r❛ q✉❛❧q✉❡r h → 0✱ P[N(h) = 1] = λh + o(h)❀ ✹✳ P❛r❛ q✉❛❧q✉❡r h → 0✱ P[N(h) > 1] = o(h)✳

      ❆ ♣r✐♠❡✐r❛ ❝♦♥❞✐çã♦ ✐♥❞✐❝❛ q✉❡ ♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s ♦❝♦rr✐❞♦s ❡♠ ❞♦✐s ✐♥t❡r✈❛❧♦s < t < t ) − N (t )

      ❞❡ t❡♠♣♦ ❞✐s❥✉♥t♦s sã♦ ✐♥❞❡♣❡♥❞❡♥t❡s✱ ✐st♦ é✱ ❞❛❞♦ t 1 2 3 ❡♥tã♦ N(t 2 1 é 3 ) − N (t ) 2 ✐♥❞❡♣❡♥❞❡♥t❡ ❞❡ N(t ✳

      ❆ s❡❣✉♥❞❛ ❝♦♥❞✐çã♦ ❡①✐❣❡ q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ N(t + h) − N(t) s❡❥❛ ✐♥❞❡♣❡♥❞❡♥t❡ ❞❡ t✱ ♦✉ s❡❥❛✱ ❞❡♣❡♥❞❡ ✉♥✐❝❛♠❡♥t❡ ❞❛ s✉❛ ❛♠♣❧✐t✉❞❡ h✳

      ❆ t❡r❝❡✐r❛ ♣r♦♣r✐❡❞❛❞❡ ✏tr❛❞✉③✑ q✉❡ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ♦❝♦rr❡r ✉♠ s✐♥✐str♦ ♥✉♠ ♣❡q✉❡♥♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ]t, t + h[ é ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ à ❞✉r❛çã♦ ❞♦ ✐♥t❡r✈❛❧♦✳

      ❆ q✉❛rt❛ ❝♦♥❞✐çã♦ ✏tr❛❞✉③✑ q✉❡ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ♦❝♦rr❡r ❞♦✐s ♦✉ ♠❛✐s s✐♥✐str♦s ♥✉♠ ♣❡q✉❡♥♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ é ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ♥✉❧❛✳ ❚❡♦r❡♠❛ ✸✳✶✳ ❙❡ {N(t)} t≥0 é ✉♠ ♣r♦❝❡ss♦ ❞❡ P♦✐ss♦♥ ❞❡ ✐♥t❡♥s✐❞❛❞❡ λ✱ ❡♥tã♦ ❛ ✈❛r✐á✲ ✈❡❧ ❛❧❡❛tór✐❛ N(t) s❡❣✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ P♦✐ss♦♥ ❞❡ ♠é❞✐❛ ❡ ✈❛r✐â♥❝✐❛ λt ❝♦♠ t > 0✱ ♦✉ s❡❥❛ k λt P (λt) e

      [N (t) = k] = , k ∈ N k! ❉❡♠♦♥str❛çã♦✳ ❆ ❞❡♠♦♥str❛çã♦ ❞❡st❡ t❡♦r❡♠❛ ♣♦❞❡ s❡r ❝♦♥s✉❧t❛❞❛✱ ♣♦r ❡①❡♠♣❧♦✱ ❡♠

      ◆❡st❡ s❡❝çã♦ ❝♦♥s✐❞❡r❛✲s❡ q✉❡ ♦ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦ é ✉♥✐tár✐♦✱ ♦✉ s❡❥❛✱ t = 1 ❡ λ é ❝♦♥st❛♥t❡ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✱ ♦✉ s❡❥❛✱ ❝♦♥s✐❞❡r❛✲s❡ q✉❡ ♥ã♦ ❤á ♠❡❧❤♦r✐❛ ♥❛ ❝♦♥❞✉çã♦ ❞♦ s❡❣✉r❛❞♦✳ ❖s ❞❛❞♦s ❞❡ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❖s ❞❛❞♦s ❢♦r♥❡❝✐❞♦s ♣❡❧❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛✱ ❝♦rr❡s♣♦♥❞❡♠ ❛♦s ❞❛❞♦s r❡❧❛t✐✈♦s ❛♦s s✐♥✐str♦s ❞❡❝❧❛r❛❞♦s ❞❛ ❝❛rt❡✐r❛ ❞❡ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❝✐✈✐❧ ❞♦ r❛♠♦ ❛✉t♦♠ó✈❡❧ ❞♦ ❛♥♦ ✷✵✵✾✳ h → = 0 f (h)

      ❯♠❛ ❢✉♥çã♦ f ❞✐③✲s❡ ✉♠ ✐♥✜♥✐tés✐♠♦ ❝♦♠ h ❡ r❡♣r❡s❡♥t❛✲s❡ ♣♦r o(h) q✉❛♥❞♦ lim 0,h6=0 ✳

      ✸✳✶ ◆ú♠❡r♦ ❞❡ ❙✐♥✐str♦s ✷✼

      ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ❛ ❞✐str✐❜✉✐çã♦ ♦❜s❡r✈❛❞❛ ❞♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s ♣❛rt✐❝✐♣❛✲ ❞♦s ❡♠ ✷✵✵✾✳ ❆♥❛❧✐s❛♥❞♦ ♦s ❞❛❞♦s ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ♠❛✐♦r ♣❛rt❡ ❞♦s s❡❣✉r❛❞♦s ♥ã♦ ❞❡❝❧❛r❛r❛♠ s✐♥✐str♦s✱ s❡♥❞♦ q✉❡ ❛ ♠é❞✐❛ ❡ ❛ ✈❛r✐â♥❝✐❛ ♦❜s❡r✈❛❞❛s ❞♦s s✐♥✐str♦s sã♦✱ r❡s✲ 2

      = 0, 200597848 ♣❡❝t✐✈❛♠❡♥t❡✱ ¯x = 0, 147553733 ❡ s ✳ ❉❛❞♦ q✉❡ ❛ ✈❛r✐â♥❝✐❛ é ♠❛✐♦r ❞♦ q✉❡ ❛ ♠é❞✐❛✱ ♣♦❞❡✲s❡ s✉s♣❡✐t❛r q✉❡ ❛ ❞✐str✐❜✉✐çã♦ P♦✐ss♦♥ ♥ã♦ s❡rá ❛ ♠❡❧❤♦r ❞✐str✐❜✉✐çã♦ ♣❛r❛ ❛❥✉st❛r ❛♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s ♣❛rt✐❝✐♣❛❞♦s✳

      ❚❛❜❡❧❛ ✸✳✶✿ ◆ú♠❡r♦ ❖❜s❡r✈❛❞♦ ❞❡ ❙✐♥✐str♦s ◆ú♠❡r♦ ❞❡ ❙✐♥✐str♦s ◆ú♠❡r♦ ❞❡ ❆♣ó❧✐❝❡s

      ✵ ✶✷✹✻✾ ✶ ✶✸✻✸ ✷ ✷✷✾ ✸ ✻✻

      ≥ ✹ ✶✼

      ❚♦t❛❧ ✶✺✻✶✾ ❆❥✉st❛♠❡♥t♦ ❆ ❡st✐♠❛t✐✈❛ ❞❡ ♠á①✐♠❛ ✈❡r♦s✐♠✐❧❤❛♥ç❛ ♣❛r❛ ♦ ♣❛râ♠❡tr♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ P♦✐ss♦♥ é ❞❛❞♦ ♣♦r ˆλ = ¯x = 0, 147553733✳ ❯t✐❧✐③❛♥❞♦ ♦ t❡st❡ ❞❡ ◗✉✐✲q✉❛❞r❛❞♦ ❞❡ P❡❛rs♦♥ ♣❛r❛ t❡st❛r ♦ ❛❥✉st❛♠❡♥t♦ ❛♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s✱ ❝♦♥s✐❞❡r❛♥❞♦ ✉♠ ♥í✈❡❧ ❞❡ s✐❣♥✐✜❝â♥❝✐❛ ❞❡ ✺✪✱ ♦❜t❡✈❡✲s❡✿

      ❚❛❜❡❧❛ ✸✳✷✿ ❚❡st❡ ❞❡ ◗✉✐✲q✉❛❞r❛❞♦ ♣❛r❛ ❛ ❞✐str✐❜✉✐çã♦ P♦✐ss♦♥ 2 k n p np k k k

      X obs ✵ ✶✷✹✻✾ ✵✱✽✻✷✽✶✻✵✵ ✶✷✷✵✶✱✻✼ ✺✱✼✾ ✶ ✶✸✻✸ ✵✱✶✷✼✸✶✶✼✸ ✶✽✵✵✱✼✵ ✶✵✻✱✹✵ ✷ ✷✷✾ ✵✱✵✵✾✸✾✷✻✻ ✶✸✷✱✽✺ ✻✾✱✺✾

      ≥ 3 ✽✸ ✵✱✵✵✵✹✼✾✺✸ ✻✱✼✽ ✽✺✻✱✹✾

      ❚♦t❛❧ ✶✹✶✹✹ ✶ ✶✹✶✹✹ ✶✵✸✽✱✷✸✻ 2 =

      ❯♠❛ ✈❡③ q✉❡ ♦ ✈❛❧♦r ♦❜s❡r✈❛❞♦ ❞❛ ❡st❛tíst✐❝❛ ❞♦ t❡st❡ ❞❡ q✉✐✲q✉❛❞r❛❞♦✱ X 2 obs 1038, 236 > X = 5, 991465 2 ✱ ❝♦♥❝❧✉✐✲s❡✱ ❝♦♠ ✉♠ ♥í✈❡❧ ❞❡ ❝♦♥✜❛♥ç❛ ❞❡ ✾✺✪✱ q✉❡ ♦ ♣r♦❝❡ss♦ ❞❡ P♦✐ss♦♥ ❤♦♠♦❣é♥❡♦ ♥ã♦ s❡ ❛❥✉st❛ ❛♦s ❞❛❞♦s✱ ♦✉ s❡❥❛✱ ♦s ❞❛❞♦s ♥ã♦ r❡✈❡✲ ❧❛♠ ❡①✐st✐r ❤♦♠♦❣❡♥❡✐❞❛❞❡ ♥♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦s s❡❣✉r❛❞♦s✳ ❏✉st✐✜❝❛✲s❡✱ ❛ss✐♠✱ ❛ ✐♥tr♦❞✉çã♦ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❝♦♠♦ ❢❡rr❛♠❡♥t❛ ❞❡ t❛r✐❢❛çã♦ ❛ ♣♦st❡r✐♦r✐✳

      ❉❛❞♦ q✉❡ s❡ r❡❥❡✐t♦✉ ❛ ❤✐♣ót❡s❡ ❞❡ q✉❡ ♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s s❡❣✉✐❛ ❛ ❞✐str✐❜✉✐çã♦

      ✷✽ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ s❡❣✉r❛❞♦s ❞❡♥tr♦ ❞❡ ❝❛❞❛ ❝❧❛ss❡ ❞❡ r✐s❝♦✱ ♥♦♠❡❛❞❛♠❡♥t❡ ✉♠ ♠♦❞❡❧♦ ❡♠ q✉❡ ❛ ✈❛r✐â♥❝✐❛ s❡❥❛ s✉♣❡r✐♦r à ♠é❞✐❛✳ ◆❡st❡ ❝❛s♦✱ ❛ t❛r✐❢❛çã♦ ❞♦ ♣ré♠✐♦ ❛ ♣♦st❡r✐♦r✐ é ♣❡r❢❡✐t❛♠❡♥t❡ ❥✉st✐✜❝á✈❡❧✳

      

    ✸✳✶✳✷ Pr♦❝❡ss♦ ❞❡ P♦✐ss♦♥ ❍❡t❡r♦❣é♥❡♦ ✲ ❈❛rt❡✐r❛ ❍❡t❡r♦❣é♥❡❛

      ❊♥q✉❛♥t♦ q✉❡ ♥♦ ♣r♦❝❡ss♦ ❞❡ P♦✐ss♦♥ ❤♦♠♦❣é♥❡♦ s❡ ✈❡r✐✜❝❛ q✉❡ ♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s s❡❣✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ P♦✐ss♦♥ ❞❡ ♣❛râ♠❡tr♦ ❝♦♥st❛♥t❡✱ λ✱ ♦ ♣r♦❝❡ss♦ ❞❡ P♦✐ss♦♥ ❤❡✲ t❡r♦❣é♥❡♦ ❝♦♥s✐❞❡r❛ q✉❡ ♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s✱ N(t)✱ s❡❣✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ P♦✐ss♦♥ ❞❡ ♣❛râ♠❡tr♦ λ✱ ❡♠ q✉❡ λ é ♦ r❡s✉❧t❛❞♦ ❞❡ ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ♥ã♦ ♥❡❣❛t✐✈❛ Λ✳ ❈♦♥s✐❞❡r❡✲s❡ q✉❡ ❛ ❢✉♥çã♦ ❞✐str✐❜✉✐çã♦ ❞❡ Λ é ❞❛❞❛ ♣♦r U (λ) = P[Λ ≤ λ].

      ✭✸✳✶✮ ❆ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ Λ é ❞❡s✐❣♥❛❞❛ ♣♦r ✈❛r✐á✈❡❧ ❞❡ ❡str✉t✉r❛ ❡ U(λ) ❛ ❞✐str✐❜✉✐çã♦

      ❞❡ ❡str✉t✉r❛✳ t≥0 ❉❡✜♥✐çã♦ ✸✳✷✳ ❖ ♣r♦❝❡ss♦ ❞❡ ❝♦♥t❛❣❡♠ ✐♥❝♦♥❞✐❝✐♦♥❛❧✱ {N(t)} ✱ t❛❧ q✉❡✿

      ✶✳ N(0) = 0 ✷✳ P P Z

      [N (t + s) − N (s) = k] = [N (t + s) − N (t) = k|λ]dU (λ) Z ∞ k − λt (λt) = e dU (λ)

      ✭✸✳✷✮ k! é ❞❡s✐❣♥❛❞♦ ♣♦r ♣r♦❝❡ss♦ ❞❡ P♦✐ss♦♥ ▼✐st♦✳

      ❉❡ ❝♦♥❝❧✉✐✲s❡ q✉❡ ♦ ♣r♦❝❡ss♦ ❞❡ P♦✐ss♦♥ ▼✐st♦ t❡♠ ✐♥❝r❡♠❡♥t♦s ❡st❛❝✐♦♥ár✐♦s ❡ ♣♦rt❛♥t♦✱ Z ∞ k − λt (λt) p (t) = P[N (t) = k] = e dU (λ) k

      ✭✸✳✸✮ k! ♦✉ s❡❥❛✱ N(t) t❡♠ ❞✐str✐❜✉✐çã♦ P♦✐ss♦♥ ▼✐st❛✳ ●❡r❛❧♠❡♥t❡✱ ❛ss✉♠❡✲s❡ q✉❡ Λ é ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❝♦♥tí♥✉❛✳ ❆s ❞✐str✐❜✉✐çõ❡s ❡str✉t✉r❛s ♠❛✐s ✉s❛❞❛s ♥❛ ♠♦❞❡❧❛çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s✱ ✈❡r sã♦ ❛ ❞✐str✐❜✉✐çã♦ ●❛♠❛ ❡ ❛ ❞✐str✐❜✉✐çã♦ ■♥✈❡rs❛ ●❛✉ss✐❛♥❛✳ ❖✉tr❛s s♦❧✉çõ❡s ♣♦❞❡♠ ♥♦ ❡♥t❛♥t♦ s❡r ❡st✉❞❛❞❛s ❡ ❛♣❧✐❝❛❞❛s✱ ✈❡r

      ✸✳✶ ◆ú♠❡r♦ ❞❡ ❙✐♥✐str♦s ✷✾ t < t < t 1 2 P ✱ t❡♠✲s❡ q✉❡ Z ∞ [N (t ) − N (t ) = k , N (t ) − N (t ) = k ] = P 1 1 2 1 2

      = [N (t ) − N (t ) = k , N (t ) − N (t ) = k |λ]dU (λ) = Z P 1 1 2 1 2 = [N (t ) − N (t ) = k |λ]P[N (t ) − N (t ) = k |λ]dU (λ) 6= Z ∞ Z ∞ P P 1 1 2 1 2

      6= [N (t ) − N (t ) = k |λ]dU (λ) [N (t ) − N (t ) = k |λ]dU (λ) = 1 1 2 1 2 = P[N (t )N (t ) = k ]P[N (t ) − N (t )]. 1 1 2 1 ✭✸✳✹✮

      ❆ ♠é❞✐❛ ❡ ❛ ✈❛r✐â♥❝✐❛ ❞❛ ❞✐str✐❜✉✐çã♦ P♦✐ss♦♥ ♠✐st❛ sã♦ ❞❛❞❛s ♣♦r E[N (t)] = tE[Λ]

      ✭✸✳✺✮ ❡ 2 2 V [N (t)] = tE[Λ] + t V [Λ ].

      ✭✸✳✻✮ ❈♦♠♦ s❡ ♣♦❞❡ ✈❡r✐✜❝❛r✱ ❛ ✈❛r✐â♥❝✐❛ é s✉♣❡r✐♦r à ♠é❞✐❛✱ ♣♦rt❛♥t♦ ❡st❡ ♠♦❞❡❧♦ r❡✢❡❝t❡

      ♠❡❧❤♦r ❛ ❤❡t❡r♦❣❡♥❡✐❞❛❞❡ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦s s❡❣✉r❛❞♦s✳ ❖ ♠♦❞❡❧♦ P♦✐ss♦♥✲●❛♠❛ ❆ ❞✐str✐❜✉✐çã♦ P♦✐ss♦♥✲●❛♠❛ é ❞❛s ♠❛✐s ✉t✐❧✐③❛❞❛s ♣❛r❛ r❡✢❡❝t✐r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❤❡✲ t❡r♦❣é♥❡♦ ♥❛ ❝♦♥❞✉çã♦ ❞♦s s❡❣✉r❛❞♦s ❞❡ ✉♠❛ ❝❛rt❡✐r❛ ❞❡ ❛♣ó❧✐❝❡s ❞♦ s❡❣✉r♦ ❛✉t♦♠ó✈❡❧ ❞❛s s❡❣✉r❛❞♦r❛s✳ ➱ ♦❜t✐❞❛ q✉❛♥❞♦ s❡ ✈❡r✐✜❝❛ q✉❡ ♦ ♣❛râ♠❡tr♦ Λ s❡ ❛❥✉st❛ ❛ ✉♠❛ ❞✐str✐❜✉✐çã♦ ●❛♠❛✳

      ❙❡♥❞♦ ❛ss✐♠✱ ❛❞♠✐t✐♥❞♦ q✉❡ Λ s❡❣✉❡ ❛ ❞✐str✐❜✉✐çã♦ ●❛♠❛ ❞❡ ♣❛râ♠❡tr♦s α ❡ β✱ ❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ Λ é ❞❛❞❛ ♣♦r

      1 α − βλ (α−1) u(λ) = β e λ , λ > 0, α > 0 e β > 0.

      ✭✸✳✼✮ Γ(α)

      ❖ ♣❛râ♠❡tr♦ α é ♦ ♣❛râ♠❡tr♦ ❞❡ ❢♦r♠❛ ❡ β ♦ ♣❛râ♠❡tr♦ ❞❡ ❡s❝❛❧❛✳ k P♦rt❛♥t♦✱ ❛ ❞✐str✐❜✉✐çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s✱ p ✱ ✈❡r é ❞❛❞❛ ♣♦r Z ∞ p k = p k (λ)u(λ)dλ Z k − λt α − βλ α−1 (λt)

      1 = e β e λ dU (λ).

      ✭✸✳✽✮ k! Γ(α)

      ✸✵ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ α k α + k − 1

      β t p k = , ✭✸✳✾✮ k β + t β + t k

      ♦✉ s❡❥❛✱ é ❡q✉✐✈❛❧❡♥t❡ ❛ ❞✐③❡r q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s✱ p ✱ s❡❣✉❡ ✉♠❛ β ❞✐str✐❜✉✐çã♦ ❇✐♥♦♠✐❛❧ ◆❡❣❛t✐✈❛✱ ❞❡ ♣❛râ♠❡tr♦s α ❡ p ❝♦♠ p = ✳ t+β

      ❆ ♠é❞✐❛ ❡ ❛ ✈❛r✐â♥❝✐❛ ❞♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s ♦❜t✐❞♦s ♣❡❧❛ ❞✐str✐❜✉✐çã♦ ❇✐♥♦♠✐❛❧ ◆❡❣❛t✐✈❛✱ ♣❛r❛ t = 1✱ sã♦ ❞❛❞❛s ♣♦r

      α E[N ] =

      ✭✸✳✶✵✮ β

      ❡ α

      1 V [N ] = 1 + .

      ✭✸✳✶✶✮ β β

      ❈♦♠♦ s❡ ♣♦❞❡ ✈❡r✐✜❝❛r✱ ❛ ✈❛r✐â♥❝✐❛ é s✉♣❡r✐♦r à ♠é❞✐❛✱ ❝♦♠♦ ❡r❛ ❞❡ ❡s♣❡r❛r✳ ❯t✐❧✐③❛♥❞♦ ♦ ♠ét♦❞♦ ❞❛ ♠á①✐♠❛ ✈❡r♦s✐♠✐❧❤❛♥ç❛ ♣❛r❛ ❛ ❡st✐♠❛çã♦ ❞♦s ♣❛râ♠❡tr♦s

      α ❡ β t❡♠✲s❡

      α ˆ ˆ

      β = ✭✸✳✶✷✮ x ¯

      ❡ ˆα é s♦❧✉çã♦ ❞❛ ❡q✉❛çã♦ X m m X

      1 1 x ¯ n + . . . + = n ln 1 + . k k ✭✸✳✶✸✮ k=0 k=0 α α + k − 1 α

      ❖ ❛❥✉st❛♠❡♥t♦ ❆s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s α✱ β ❡ p ❞❛ ❞✐str✐❜✉✐çã♦ ❇✐♥♦♠✐❛❧ ◆❡❣❛t✐✈❛✱ ✉t✐❧✐③❛♥❞♦ ♦ ♠ét♦❞♦ ❞❛ ♠á①✐♠❛ ✈❡r♦s✐♠✐❧❤❛♥ç❛✱ ❛♣r❡s❡♥t❛♠✲s❡ ♥❛ ❚❛❜❡❧❛

      ❚❛❜❡❧❛ ✸✳✸✿ P❛râ♠❡tr♦s ❞❛ ❇✐♥♦♠✐❛❧ ◆❡❣❛t✐✈❛ ˆ

      α ˆ β p ˆ ✵✱✹✵✽✷✵✼ ✷✱✼✻✻✺ ✵✱✼✸✹✺✵✶✺✷✼

      ❖❜s❡r✈❛♥❞♦ ❛ ❚❛❜❡❧❛ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦ ✈❛❧♦r ♦❜s❡r✈❛❞♦ ❞❛ ❡st❛tíst✐❝❛ ❞♦ t❡st❡ 2 2 = 5, 183430005 < χ = 5, 991465

      ❞❡ ◗✉✐✲q✉❛❞r❛❞♦ ❞❡ P❡❛rs♦♥ é ❞❛❞♦ ♣♦r X ✱ ♦ q✉❡ obs 2 ❡q✉✐✈❛❧❡ ❛ ✉♠ ♣✲✈❛❧✉❡≃ 0, 075 ❝♦♥❝❧✉✐♥❞♦✲s❡✱ ♣♦rt❛♥t♦✱ q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❇✐♥♦♠✐❛❧ ◆❡❣❛t✐✈❛ s❡ ❛❥✉st❛ ❛♦s ❞❛❞♦s ♦❜s❡r✈❛❞♦s ❞♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s✱ ♣❛r❛ ✉♠ ♥í✈❡❧ ❞❡ s✐❣✲ ♥✐✜❝â♥❝✐❛ ❞❡ ✺✪✳

      ✸✳✷ ❙✐st❡♠❛ ❇♦♥✉s ▼❛❧✉s ❆❝t✉❛❧ ❞❛ ●❛r❛♥t✐❛ ✸✶ ❚❛❜❡❧❛ ✸✳✹✿ ❚❡st❡ ❞♦ ◗✉✐✲q✉❛❞r❛❞♦ ♣❛r❛ ❛ ❞✐str✐❜✉✐çã♦ ●❛♠❛ 2 k n p n k k p k

      X obs ✵ ✶✷✹✻✾ ✵✱✽✽✶✺✻✼✶✾✾ ✶✷✹✻✽✱✽✾ 0, 00001034 ✶ ✶✸✻✸ ✵✱✵✾✺✻✽✶✽✹✽ ✶✸✺✸✱✸✷ ✵✱✵✻✾✶✽✵✺✼ ✷ ✷✷✾ ✵✱✵✶✼✽✹✸✵✹✽ ✷✺✷✱✸✼ ✷✱✶✻✹✹✼✼✾✺✺ ✸ ✻✻ ✵✱✵✵✸✼✾✶✵✸✶ ✺✸✱✻✷ ✷✱✽✺✽✶✻✻✷✸

      ≥ 4 ✶✼ ✵✱✵✵✶✶✶✻✽✼✸ ✶✺✱✽✵ ✵✱✵✾✶✻✵✹✷✶✻

      ❚♦t❛❧ ✶✹✶✹✹ ✶ ✶✹✶✹✹ ✺✱✶✽✸✹✸✵✵✵✺

      ✸✳✷ ❙✐st❡♠❛ ❇♦♥✉s ▼❛❧✉s ❆❝t✉❛❧ ❞❛ ●❛r❛♥t✐❛

      ❖ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ♣❛r❛ ♦ ❙❡❣✉r♦ ❆✉t♦♠ó✈❡❧ ❞❡ ❘❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❈✐✈✐❧ q✉❡

      ♦

      ❛❝t✉❛❧♠❡♥t❡ ✈✐❣♦r❛ ♥❡ss❛ ❙❡❣✉r❛❞♦r❛ é r❡❣✐❞♦ ♣❡❧♦ ❉❡❝r❡t♦ ▲❡✐ ♥ ✶✼✲✷✵✵✸✳

      ✸✳✷✳✶ ❉❡✜♥✐çã♦

      ❖ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ✉t✐❧✐③❛❞♦ ♥❡st❛ s❡❣✉r❛❞♦r❛✱ ♣❛r❛ ♦ s❡❣✉r♦ ❞❡ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❝✐✈✐❧ ❛✉t♦♠ó✈❡❧✱ é ❝❛r❛❝t❡r✐③❛❞♦ ♣❡❧❛s s❡❣✉✐♥t❡s r❡❣r❛s ❞❡ tr❛♥s✐çã♦✿

      ❆s ❛♣ó❧✐❝❡s ❝♦♠ ✶✱ ✷✱ ✸ ♦✉ ✹ s✐♥✐str♦s ❞❡❝❧❛r❛❞♦s ♥✉♠❛ ❛♥✉✐❞❛❞❡ s♦❢r❡♠✱ ♥❛

    • ❛♥✉✐❞❛❞❡ s❡❣✉✐♥t❡✱ ✉♠ ❛❣r❛✈❛♠❡♥t♦ ❞❡ ✶✺✪✱ ✸✵✪✱ ✹✺✪ ♦✉ ✶✵✵✪✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ s♦❜r❡ ♦ ♣ré♠✐♦ ❛ ♣r✐♦r✐✳ ❖ ♣ré♠✐♦ ❞❛s ❛♣ó❧✐❝❡s ❝♦♠ ✺ ♦✉ ♠❛✐s s✐♥✐str♦s ❞❡❝❧❛r❛❞♦s ♥✉♠❛ ❛♥✉✐❞❛❞❡ é ❛♥❛❧✐s❛❞♦ ❝❛s♦ ❛ ❝❛s♦✳ ❆s ❛♣ó❧✐❝❡s q✉❡ s❡ ❡♥❝♦♥tr❡♠ ✷ ❛♥♦s ❝♦♥s❡❝✉t✐✈♦s s❡♠ ♣❛rt✐❝✐♣❛r s✐♥✐str♦s ❜❡♥❡✜❝✐❛rã♦ ❞❡ ✉♠ ❞❡s❝♦♥t♦ ❞❡ ✸✵✪ s♦❜r❡ ♦ ♣ré♠✐♦ ❛ ♣r✐♦r✐✳

      P♦r ✉♠❛ q✉❡stã♦ ❞❡ s✐♠♣❧✐✜❝❛çã♦✱ ♥❡st❡ tr❛❜❛❧❤♦✱ ❝♦♥s✐❞❡r❛r❡♠♦s q✉❡ ❛s ❛♣ó❧✐❝❡s ❝♦♠ ✺ ♦✉ ♠❛✐s s✐♥✐str♦s ❞❡❝❧❛r❛❞♦s ♥✉♠❛ ❛♥✉✐❞❛❞❡✱ t❡rã♦ ✉♠ ❛❣r❛✈❛♠❡♥t♦ ❞❡ ✶✵✵✪ ❞♦ ♣ré♠✐♦ ❛ ♣r✐♦r✐✳

      ❚❡♥❞♦ ❡♠ ❝♦♥t❛ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ SBM ❥á ❞❡✜♥✐❞❛s ❡ ❝♦♥s✐❞❡r❛♥❞♦ ♦ ❞❡s❞♦✲ ❜r❛♠❡♥t♦ ❞❛s ❝❧❛ss❡s ❞❡ ❢♦r♠❛ ❛ ❣❛r❛♥t✐r q✉❡ ♦ SBM é r❡♣r❡s❡♥t❛❞♦ ♣♦r ✉♠❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈✱ ✈❡r ❛s ❝❧❛ss❡s ❞♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛✱ q✉❡ ❝♦rr❡s♣♦♥❞❡♠ ❛♦s ❡st❛❞♦s ❞❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈✱ sã♦ ❞❡✜♥✐❞❛s ♥❛ ❚❛❜❡❧❛ 1

      ❖ ❡st❛❞♦ i ✐♥❞✐❝❛ q✉❡ ♦ s❡❣✉r❛❞♦ s❡ ❡♥❝♦♥tr❛ ♥❛ ❈❧❛ss❡ i ♣❡❧♦ ♣r✐♠❡✐r♦ ❛♥♦✱ ❡♥✲ 2 q✉❛♥t♦ q✉❡✱ i ✐♥❞✐❝❛ q✉❡ ♦ s❡❣✉r❛❞♦ s❡ ❡♥❝♦♥tr❛ ♥❛ ❈❧❛ss❡ i ♣❡❧♦ s❡❣✉♥❞♦ ❛♥♦ ❝♦♥s❡✲ ❝✉t✐✈♦✱ ❝♦♠ i = 2, . . . , 6✳

      ❖ ✈❡❝t♦r ❞♦s ♣ré♠✐♦s é ❞❛❞♦ ♣♦r T b = (70 100 100 115 115 130 130 145 145 200 200).

      ✭✸✳✶✹✮

      ✸✷ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❚❛❜❡❧❛ ✸✳✺✿ ❈❧❛ss❡s ❞♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❞❛ ●❛r❛♥t✐❛

      ❈❧❛ss❡ ❉❡s❝♦♥t♦ ✈s✳ ❆❣r❛✈❛♠❡♥t♦ ✶ ✸✵✪ ❉❡s❝♦♥t♦

      2 2 ✵✪ ❉❡s❝♦♥t♦

      2 1 ✵✪ ❉❡s❝♦♥t♦

      3 2 ✶✺✪ ❆❣r❛✈❛♠❡♥t♦

      3 1 ✶✺ ✪ ❆❣r❛✈❛♠❡♥t♦

      4 2 ✸✵ ✪ ❆❣r❛✈❛♠❡♥t♦

      4 1 ✸✵ ✪ ❆❣r❛✈❛♠❡♥t♦

      5 2 ✹✺ ✪ ❆❣r❛✈❛♠❡♥t♦

      5 1 ✹✺ ✪ ❆❣r❛✈❛♠❡♥t♦

      6 2 ✶✵✵ ✪ ❆❣r❛✈❛♠❡♥t♦

      6 1 ✶✵✵ ✪ ❆❣r❛✈❛♠❡♥t♦

      ❆ ♠❛tr✐③ ❞❛s r❡❣r❛s ❞❡ tr❛♥s✐çõ❡s✱ T ✱ é ❞❡✜♥✐❞❛ ♣♦r✿ 2 2 2 1 1 {0} − − − {1} − {2} − {3} − {4, 5, . . .} {0} − − − {1} − {2} − {3} − {4, 5, . . .} − {0} − − {1} − {2} − {3} − {4, 5, . . .} 1 2 2 2 1 3 2 3 1 4 2 4 1 5 2 5 1 6 2 6 1 4 3

      3 2 1 2 {0} − − − {1} − {2} − {3} − {4, 5, . . .} {0} − − − {1} − {2} − {3} − {4, 5, . . .} − − − {0} {1} − {2} − {3} − {4, 5, . . .}

      T = 4 6 5 6 5 1 1 2 2 1 {0} − − − {1} − {2} − {3} − {4, 5, . . .} {0} − − − {1} − {2} − {3} − {4, 5, . . .} − − − − {1} {0} {2} − {3} − {4, 5, . . .} − − − − {1} − {2} {0} {3} − {4, 5, . . .} − − − − {1} − {2} − {3} {0} {4, 5, . . .} .

      ❚❡♥❞♦ ❡♠ ❝♦♥t❛ ❛ ♠❛tr✐③ ❞❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦ T ✱ ❛ ♠❛tr✐③ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ tr❛♥s✐çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❝❧áss✐❝♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐s✲ tr❛❧✐❞❛❞❡ λ✱ é ❞❛❞❛ ♣♦r✿ 2 2 p p 1 p p 2 1   •   • 1 p p p p p 2 2 2 1 3 2 3 1 p 1 1 p 1 4 2 4 1 2 p 2 p 2 2 5 5 3 p 1 3 3 p 6 2 6 1

      3 3 4 1 p p 2 p p 2 p p   •   • 1 p 1 p 1 p 2 p 2 p 2 p 3 p 3 p 3 p

      P = T ,λ 4 6 5   5  6 2 p p 1 1 p 2 1 p   • p p p 1 p 1 p p 1 p 1 p 1 p 2 p 2 p 2 p 2 p 3 p p 2 p p 3 p 3 p 3 p 3 p

      k k = P[N = k] = e , k ∈ N = 1 − p k λ λ • P 3

      ♦♥❞❡ p ❡ p ✳ k=0 k! ❖ s✐st❡♠❛ ❛ss✐♠ ❞❡✜♥✐❞♦ ♣♦❞❡ s❡r ❝♦♥s✐❞❡r❛❞♦ ❝♦♠♦ ✉♠❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈✳ ❆♥❛✲

      ❧✐s❛♥❞♦ ❛ ♠❛tr✐③ ❞❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦✱ ❝♦♥❝❧✉✐✲s❡ q✉❡ ♥ã♦ s❡ tr❛t❛ ❞❡ ✉♠❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈ ✐rr❡❞✉tí✈❡❧✱ ✐st♦ ♣♦rq✉❡ ❛ ❝❧❛ss❡ 2 ✱ q✉❡ r❡♣r❡s❡♥t❛ ❛ ❝❧❛ss❡ ❞❡ ❡♥tr❛❞❛✱ ♥ã♦ é 2

      ✸✳✷ ❙✐st❡♠❛ ❇♦♥✉s ▼❛❧✉s ❆❝t✉❛❧ ❞❛ ●❛r❛♥t✐❛ ✸✸ 1 ❞❛ ❝❧❛ss❡ 2 ✳ ➱✱ ♣♦rt❛♥t♦✱ ✉♠❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈ ❝♦♠ ❞✉❛s ❝❧❛ss❡s ❞❡ ❝♦♠✉♥✐❝❛çã♦✿ C = {2 , 2 } = {1, 3 , 3 , 4 , 4 , 5 , 5 , 6 , 6 } 1 1 2 2 1 2 1 2 1 2 1 2

      ❡ C ✳ ➱ r❡❧❡✈❛♥t❡ ❛❧❡rt❛r ❞❡s❞❡ ❥á q✉❡ ❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦✱ ❛ss✐♠ ❞❡✜♥✐❞❛s✱ ♣r❡❥✉❞✐❝❛♠

      ❛ ❛❝t✐✈✐❞❛❞❡ ❞❛ ❙❡❣✉r❛❞♦r❛✳ ◆♦t❡✲s❡ q✉❡✱ ♣♦r ❡①❡♠♣❧♦✱ ♣❛r❛ ✉♠ s❡❣✉r❛❞♦ q✉❡ s❡ ❡♥❝♦♥tr❡ ♥❛ ❝❧❛ss❡ ❝♦♠ ✶✵✵✪ ❞❡

      ❛❣r❛✈❛♠❡♥t♦ r❡✈❡❧❛✲s❡ s❡r ♠❛✐s ✈❛♥t❛❥♦s♦ ♣❛rt✐❝✐♣❛r ✉♠ s✐♥✐str♦ ♥❛ ❛♥✉✐❞❛❞❡ s❡❣✉✐♥t❡ ❞♦ q✉❡ ♥ã♦ ♣❛rt✐❝✐♣❛r ♥❡♥❤✉♠✳ ❙♦❜ ♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞❛ ❙❡❣✉r❛❞♦r❛✱ ✐st♦ ✐♠♣❧✐❝❛ ♦ ♣❛❣❛♠❡♥t♦ ❞❡ ♠❛✐s ✉♠❛ ✐♥❞❡♠♥✐③❛çã♦✱ ❜❡♠ ❝♦♠♦ ❛ r❡❞✉çã♦ ❞♦ ♣ré♠✐♦ ❛♦ s❡❣✉r❛❞♦ ♥❛ ❛♥✉✐❞❛❞❡ s❡❣✉✐♥t❡✳

      ❆s r❡❣r❛s ❞❡ tr❛♥s✐çã♦ ✉t✐❧✐③❛❞❛s ♥ã♦ r❡✢❡❝t❡♠ ✉♠ SBM ❥✉st♦ ❡ ❡q✉✐t❛t✐✈♦ ♣❛r❛ ♥❡✲ ♥❤✉♠❛ ❞❛s ♣❛rt❡s✱ ❜❡♠ ❝♦♠♦ ❢♦♠❡♥t❛♠ ❛ ♣❛rt✐❝✐♣❛çã♦ ❞❡ s✐♥✐str♦s ❞❡ ♠♦❞♦ ❛ ❞✐♠✐♥✉✐r ♦ ❛❣r❛✈❛♠❡♥t♦ ❞♦ ♣ré♠✐♦✳ ■st♦ ❝♦♥tr❛❞✐③ ♦ ♣r✐♥❝í♣✐♦ s✉❜❥❛❝❡♥t❡ ❛♦s SBM✳

      ◆♦ q✉❡ s❡ s❡❣✉❡✱ ❡❢❡❝t✉❛r✲s❡✲á ✉♠❛ ❛♥á❧✐s❡ ❛♦ SBM ❛❝t✉❛❧ ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛✱

      ♦

      ❝♦♠ ❛s r❡❣r❛s ❡st❛❜❡❧❡❝✐❞❛s ♣❡❧♦ ❉❡❝r❡t♦✲▲❡✐ ♥ ✶✼✴✷✵✵✸✱ s♦❜ ❛ ♣❡rs♣❡❝t✐✈❛ ❝❧áss✐❝❛ ✭❝♦♥✲ s✐❞❡r❛♥❞♦ q✉❡ ❛ ❝❛rt❡✐r❛ é ❢❡❝❤❛❞❛✮ ❡ r❡❝♦rr❡♥❞♦ ❛♦ ♠♦❞❡❧♦ ❞♦s ❱órt✐❝❡s ❊st♦❝ást✐❝♦s ✭♦♥❞❡ s❡ ❝♦♥s✐❞❡r❛ q✉❡ ❛ ❝❛rt❡✐r❛ é ❛❜❡rt❛✮✳

      ❘❡ss❛❧✈❛✲s❡ ♥♦ ❡♥t❛♥t♦✱ ❞❡s❞❡ ❥á✱ q✉❡ s❡ ❝♦♥s✐❞❡r❛ ♦ ♠♦❞❡❧♦ ❛❜❡rt♦ ❝♦♠♦ ✏♠❡❧❤♦r✑ r❡♣r❡s❡♥t❛t✐✈♦ ❞❛ r❡❛❧✐❞❛❞❡✳

      ✸✳✷✳✷ ❉✐str✐❜✉✐çã♦ ▲✐♠✐t❡✿ ❈❛rt❡✐r❛ ❋❡❝❤❛❞❛

      ❈♦♠♦ ❥á ❢♦✐ r❡❢❡r✐❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈ ✐♠♣❧í❝✐t❛ ♥♦ ♠♦❞❡❧♦ ❝❧áss✐❝♦ ♥ã♦ 1 2 é ✉♠❛ ❝❛❞❡✐❛ ✐rr❡❞✉tí✈❡❧✳ ❖ ❝♦♥❥✉♥t♦ ❞❛s ❝❧❛ss❡s ❞❡ ❜♦♥✉s 2 ❡ 2 ❢♦r♠❛♠ ✉♠❛ ❝❧❛ss❡ ❞❡ ❝♦♠✉♥✐❝❛çã♦ tr❛♥s✐❡♥t❡ ❡ ❛s r❡st❛♥t❡s ❝❧❛ss❡s ❢♦r♠❛♠ ✉♠❛ ❝❧❛ss❡ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❞❡ ❡st❛❞♦s r❡❝♦rr❡♥t❡s ♣♦s✐t✐✈♦s ❡ ❛♣❡r✐ó❞✐❝♦s✳ ❚r♦❝❛♥❞♦ ❛s ❧✐♥❤❛s ❡ ❝♦❧✉♥❛s✱ ✈❡r ❛ ♠❛tr✐③ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ tr❛♥s✐çã♦ ❡♥tr❡ ❛s ❝❧❛ss❡s ♣♦❞❡ s❡r ❡s❝r✐t❛ ♥❛ ❢♦r♠❛

      P P 1,(T ,λ) 3,(T ,λ) P = T ,λ 1,(T ,λ) P 2,(T ,λ)

      ♦♥❞❡ ❛ ♠❛tr✐③ P é ❛ ♠❛tr✐③ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ tr❛♥s✐çã♦ ❡♥tr❡ ❛s ❝❧❛ss❡s ❞❡ ❜♦♥✉s

      2 1 2 2,(T ,λ) ❡ 2 ✭❡st❛❞♦s tr❛♥s✐❡♥t❡s✮✱ P ❛ ♠❛tr✐③ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❡♥tr❡ ❛s ❝❧❛ss❡s ❞❡ ❜♦♥✉s

      {1, 3 , 3 , 4 , 4 , 5 , 5 , 6 , 6 } 1 2 1 2 1 2 1 2 3,(T ,λ) ✱ P ❛ ♠❛tr✐③ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ tr❛♥s✐çã♦ ❞❛s ❝❧❛ss❡s

      ❞❡ ❜♦♥✉s 2 1 ❡ 2 2,(T ,λ) 2 ♣❛r❛ ❛s r❡st❛♥t❡s ❝❧❛ss❡s ❞❡ ❜♦♥✉s✳ ❆ ♠❛tr✐③ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ tr❛♥s✐çã♦ P é ✉♠❛ ♠❛tr✐③ ❞❡ ❡st❛❞♦s r❡❝♦rr❡♥t❡s ♣♦s✐t✐✈♦s ❡ ❛♣❡r✐ó❞✐❝♦s✱ ♦✉ s❡❥❛✱ ❢♦r♠❛ ✉♠❛ ❝❧❛ss❡ ✐rr❡❞✉tí✈❡❧✱ ♣♦rt❛♥t♦ ❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ ❝♦✐♥❝✐❞❡ ❝♦♠ ❛ ❞✐str✐❜✉✐çã♦ ❡st❛❝✐♦♥ár✐❛✱ ♦✉ s❡❥❛✱ (n) n→+∞ lim p (i, j) = π 2,(T ,λ) (j), j ∈ C 2,(T ,λ) 2 P

      (j) ≥ 0, ∀j ∈ C 2 , P π (j) = 1 = π ❝♦♠ π 2,(T ,λ) 2,(T ,λ) ❡ π 2,(T ,λ) 2,(T ,λ) 2,(T ,λ) ✳ P♦rt❛♥t♦✱ (n) ❝❛❞❛ ❧✐♥❤❛ ❞❛ ♠❛tr✐③ P t❡♥❞❡ ♣❛r❛ ♦ ✈❡❝t♦r ♣ró♣r✐♦ ❡sq✉❡r❞♦ ❛ss♦❝✐❛❞♦ ❛♦ ✈❛❧♦r 2,(T ,λ) ♣ró♣r✐♦ ✶ ❞❛ ♠❛tr✐③ P ✳

      ✸✹ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ (n−2) (n) (P P + P P ) lim P 1,(T ,λ) 3,(T ,λ) 3,(T ,λ) 2,(T ,λ) n→+∞ 2,(T ,λ) n→+∞ lim P = T (n) P (n) n→+∞ lim 2,(T ,λ)

      ❡♥tã♦✱ q✉❛♥❞♦ n t❡♥❞❡ ♣❛r❛ ✐♥✜♥✐t♦✱ P T t❡♥❞❡ ♣❛r❛ ✉♠❛ ♠❛tr✐③ ❝♦♠ ❛s ❧✐♥❤❛s t♦❞❛s (T ,λ) 2,(T ,λ) = [0, π ] ✐❣✉❛✐s ❡ ❞❛ ❢♦r♠❛ π ✳

      ❆ss✐♠✱ ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ ♣❛r❛ ✉♠ s❡❣✉r❛❞♦ r❡t✐r❛❞♦ ❛♦ ❛❝❛s♦ ❞❛ ❝❛rt❡✐r❛ ❞❛s ❛♣ó❧✐❝❡s ❜❛st❛ ❝♦♥s✐❞❡r❛r ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❡str✉t✉r❛✱ ❡ ❛ ❞✐str✐❜✉✐çã♦ ✈❡♠ ❞❛❞❛ ♣♦r✿ Z π T (j) = π (j)dU (λ) , j ∈ C ∪ C . (T ,λ) 1 2

      ✭✸✳✶✺✮ P❛r❛ ❛ ♦❜t❡♥çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡✱ r❡❝♦rr❡✉✲s❡ ❛ ♠ét♦❞♦s ♥✉♠ér✐❝♦s✱ ♦✉ s❡❥❛✱ r❡❝♦rr❡✉✲s❡ à ❞✐s❝r❡t✐③❛çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❡str✉t✉r❛✱ ♦❜t❡♥❞♦✲s❡ ❛ss✐♠ ✉♠❛ ❞✐s✲ tr✐❜✉✐çã♦ ❛♣r♦①✐♠❛❞❛ ❡ ❞✐s❝r❡t❛✱ ✉t✐❧✐③❛♥❞♦ ♦ ♠ét♦❞♦ ❞❡ ❛rr❡❞♦♥❞❛♠❡♥t♦ à ✉♥✐❞❛❞❡ ♠❛✐s ♣ró①✐♠❛✳

      ❆ss✐♠✱ ❛❞❛♣t❛♥❞♦ ❛♦ ❝❛s♦ ❞✐s❝r❡t♦✱ ❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ s❡rá ❞❛❞❛ ❛tr❛✈és ❞❡✿ X d d π T (j) = π (j)u , j ∈ C ∪ C λ (T ,λ) λ ✭✸✳✶✻✮ 1 2 s❡♥❞♦ u ♦ ✈❡❝t♦r ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❛ ❞✐str✐❜✉✐çã♦ ●❛♠❛ ❞✐s❝r❡t✐③❛❞❛ ♣❛r❛ λ λ = 0.01, 0.02, . . . , 1.

      ◆♦t❡✲s❡ q✉❡✱ t❡♥❞♦ Λ ❞✐str✐❜✉✐çã♦ ●❛♠❛✱ ❝♦♠ ♦s ♣❛râ♠❡tr♦s ✐♥❞✐❝❛❞♦s ♥❛ ❚❛❜❡❧❛ t❡♠✲s❡ P[Λ ≤ 1] = 0.9865✳

      ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ ♣❛r❛ ✉♠ s❡❣✉r❛❞♦ r❡t✐r❛❞♦ ❛♦ ❛❝❛s♦ ❞❛ ❝❛rt❡✐r❛ ❞❡ ❛♣ó❧✐❝❡s✳

      ❚❛❜❡❧❛ ✸✳✻✿ ❉✐str✐❜✉✐çã♦ ▲✐♠✐t❡ ♥♦ ▼♦❞❡❧♦ ❋❡❝❤❛❞♦✿ ❙✳ ❆❝t✉❛❧ j π T (j) ✶ ✵✱✼✾✽✵✶✶✷✺✺

      2 2

      2 1

      3 2 ✵✱✵✼✵✽✷✾✼✶

      3 1 ✵✱✵✾✼✻✶✽✵✺✷

      4 2 ✵✱✵✶✵✷✸✽✾✾✹

      4 1 ✵✱✵✶✼✸✹✼✽✶✼

      5 2 ✵✱✵✵✶✻✻✻✸✷✽

      5 1 ✵✱✵✵✸✷✽✵✼✻✷

      6 2 ✵✱✵✵✵✸✶✹✸✽✸

      6 1 ✵✱✵✵✵✻✾✷✻✾✽

      1 ❚♦t❛❧

      ✸✳✷ ❙✐st❡♠❛ ❇♦♥✉s ▼❛❧✉s ❆❝t✉❛❧ ❞❛ ●❛r❛♥t✐❛ ✸✺ ❆ ♣❛rt✐r ❞❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ ❡st✐♠❛✲s❡ q✉❡✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ❧♦♥❣♦ ♣r❛③♦✱ ✼✾✱✽✪

      ❞❛s ❛♣ó❧✐❝❡s ❞❛ ❝❛rt❡✐r❛ s❡ ❡♥❝♦♥tr❛rã♦ ♥❛ ❝❧❛ss❡ ❜♦♥✐✜❝❛❞❛ ❞♦ s✐st❡♠❛ ✭❈❧❛ss❡ ✶✮ ❡ ❛♣❡♥❛s ✵✱✵✻✾✸✪ s❡ ❡♥❝♦♥tr❛rã♦ ♥❛ ❝❧❛ss❡ ♠❛✐s ❛❣r❛✈❛❞❛ ❞♦ s✐st❡♠❛ ✭❈❧❛ss❡ 6 1 ✮✳

      ❆♥❛❧✐s❛♥❞♦ ❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ ♦❜t✐❞❛ ❡st✐♠❛✲s❡ q✉❡✱ ♥❛ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ❡①✐st✐rá ✉♠❛ ❣r❛♥❞❡ ❛❣❧♦♠❡r❛çã♦ ❞❡ ❛♣ó❧✐❝❡s ♥❛ ❝❧❛ss❡ ❜♦♥✐✜❝❛❞❛ ❞♦ s✐st❡♠❛✱ s❡♥❞♦ q✉❡ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠❛ ❛♣ó❧✐❝❡ s❡ ❡♥❝♦♥tr❛r ♥✉♠❛ ❞❛s ❝❧❛ss❡s ❛❣r❛✈❛❞❛s é ♠✉✐t♦ r❡❞✉③✐❞❛✳ ❖ ♣ré♠✐♦ ♠é❞✐♦✱ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ❝♦rr❡s♣♦♥❞❡ ❛ ✼✾✱✼✹✪ ❞♦ ♣ré♠✐♦ ❛ ♣r✐♦r✐✳

      ❋✐❣✉r❛ ✸✳✶✿ ❊✈♦❧✉çã♦ ❞♦ P M ✲ ▼♦❞❡❧♦ ❋❡❝❤❛❞♦✿ ❙✳ ❆❝t✉❛❧ ❆ ✜❣✉r❛ ✐❧✉str❛ ❛ ❡✈♦❧✉çã♦ ❞♦ ♣ré♠✐♦ ♠é❞✐♦ ❞❡ ✉♠ ♥♦✈♦ s❡❣✉r❛❞♦ r❡t✐r❛❞♦ ❛♦

      ❛❝❛s♦ ❞❛ ❝❛rt❡✐r❛ ❞❡ ❛♣ó❧✐❝❡s ♥♦s ♣ró①✐♠♦s ✷✵ ❛♥♦s✳ ❆♥❛❧✐s❛♥❞♦ ♦ ❣rá✜❝♦✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦ ♣ré♠✐♦ ♠é❞✐♦ ❡stá ♣ró①✐♠♦ ❞❛ ❡st❛❝✐♦♥❛r✐❞❛❞❡ ❧♦❣♦ ♥♦ s❡❣✉♥❞♦ ❛♥♦✱ ❢❛❝t♦ ❡st❡ ❞❡✈✐❞♦ à r❛♣✐❞❡③ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈ ♣❛r❛ ❛ ❡st❛❝✐♦♥❛r✐❞❛❞❡✳

      ✸✳✷✳✸ ❉✐str✐❜✉✐çã♦ ▲✐♠✐t❡✿ ❈❛rt❡✐r❛ ❆❜❡rt❛

      ❙♦❜ ❛ ♣❡rs♣❡❝t✐✈❛ ❞❡ ✉♠❛ ❝❛rt❡✐r❛ ❛❜❡rt❛ ❛ ♠❛tr✐③ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ tr❛♥s✐çã♦ é✱ ❝♦♠♦ ✈✐♠♦s ♥❛ ❙✉❜✲s❡❝çã♦

      K q 1 P T = .

      1 ◆❡st❛ ♣❡rs♣❡❝t✐✈❛✱ ❤á q✉❡ t❡r ❡♠ ❝♦♥t❛ ❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ ❛♥✉❧❛çã♦ ❞❛s ❛♣ó❧✐❝❡s✳ 1 (j), j ∈ C ∪ C 1 2

      ❈♦♥s✐❞❡r❛♥❞♦ q ✱ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❝♦♥❞✐❝✐♦♥❛❞❛ ❞❡ ✉♠ s❡❣✉r❛❞♦ ❛❜❛♥❞♦♥❛r ❛ s❡❣✉r❛❞♦r❛✱ ❞❛❞♦ q✉❡ s❡ ❡♥❝♦♥tr❛ ♥❛ ❝❧❛ss❡ j ❞♦ s✐st❡♠❛✱ ♣❛r❛ ✉♠❛ ❞❛❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ λ✱ ❡st❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ♣♦❞❡♠ s❡r ❡st✐♠❛❞❛s r❡❝♦rr❡♥❞♦ ❛♦s ❞❛❞♦s ❞❛ ❙❡❣✉r❛❞♦r❛✱ t❡♥❞♦ ❡♠ ❝♦♥t❛ q✉❡ X q (j) = p (λ)q (j), j ∈ C ∪ C . 1 k 1,k,λ 1 2 k=0

      ✭✸✳✶✼✮ (λ)

      ♦♥❞❡ p r❡♣r❡s❡♥t❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ s❡❣✉r❛❞♦✱ ❝♦♠ ✉♠❛ ❞❛❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ 1,k,λ

      ✸✻ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❝✐♦♥❛❞❛ ❞❡ ✉♠ s❡❣✉r❛❞♦ ❛❜❛♥❞♦♥❛r ❛ ❙❡❣✉r❛❞♦r❛✱ s❛❜❡♥❞♦ q✉❡ s❡ ❡♥❝♦♥tr❛ ♥❛ ❝❧❛ss❡ j ❡ ❞❡❝❧❛r♦✉ k s✐♥✐str♦s ♥❡ss❛ ❛♥✉✐❞❛❞❡✱ ♣❛r❛ ✉♠ ❞❡t❡r♠✐♥❛❞♦ λ✳

      ❙❡♥❞♦ ❛ss✐♠✱ ❛ ♠❛tr✐③ K ❞❡✈❡rá s❡r ❝♦♥str✉í❞❛ ♣♦r ❢♦r♠❛ q✉❡ ❛ s♦♠❛ ❞❡ t♦❞♦s T ♦s ❡❧❡♠❡♥t♦s ❞❡ ❝❛❞❛ ❧✐♥❤❛ ❞❛ ♠❛tr✐③ P s❡❥❛ ✐❣✉❛❧ ❛ ✶✳ ❖s ❡❧❡♠❡♥t♦s ❞❛ ♠❛tr✐③ K ❞❡✈❡rã♦ r❡✢❡❝t✐r ❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ tr❛♥s✐çã♦ ❡♥tr❡ ❝❧❛ss❡s✱ ♣❛r❛ ♦s s❡❣✉r❛❞♦s q✉❡ ♥ã♦ ❛❜❛♥❞♦♥❛♠ ❛ s❡❣✉r❛❞♦r❛✳ ❉❡st❛ ❢♦r♠❛✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ t❡r✲s❡✲à✿ k(i, j) = p (i, j)(1 − q (i)) = T ,λ 1 = P [Z = j | Z = i, Λ = λ] (1 − q (i)), i, j ∈ C ∪ C . ∆,n+1 ∆,n 1 1 2

      ❆ ♠❛tr✐③ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ tr❛♥s✐çã♦ ♥❛s ❝❧❛ss❡s tr❛♥s✐❡♥t❡s ❞♦ s✐st❡♠❛ ❣❛r❛♥t❡ ❛ss✐♠ q✉❡ ✉♠ s❡❣✉r❛❞♦✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦ T ✱ tr❛♥s✐t❡ ❞❛ ❝❧❛ss❡ i ♣❛r❛ ❝❧❛ss❡ j✱ ❝❛s♦ ♥ã♦ ❛❜❛♥❞♦♥❡ ❛ ❙❡❣✉r❛❞♦r❛✱ ❡ ❛ s♦♠❛ ❞❡ t♦❞♦s ♦s ❡❧❡♠❡♥t♦s ❞❡ ❝❛❞❛ T ❧✐♥❤❛ ❞❛ ♠❛tr✐③ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ tr❛♥s✐çã♦ P s❡❥❛ ✶✳

      ❖s ❞❛❞♦s ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ s❛í❞❛ r❡❢❡r❡♠✲s❡ ❛♣❡♥❛s ❛♦s ú❧t✐♠♦s ✸ ❛♥♦s✱ ♦ q✉❡ ❝♦♥s✐❞❡r❛♠♦s ✐♥s✉✜❝✐❡♥t❡✳ ❆ ❡st✐♠❛çã♦ ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ s❛í❞❛ ❢♦r❛♠ ❞❡t❡r♠✐♥❛❞❛s✱ ❝♦♥s✐❞❡r❛♥❞♦✲❛s ✐♥❞❡♣❡♥❞❡♥t❡s ❞❡ λ ❡ k ❡ ❝♦♠ ❜❛s❡ ♥❛ ✐♥❢♦r♠❛çã♦ ❞✐s♣♦♥í✈❡❧ ♦❜t✐✈❡r❛♠✲s❡ ❛s ❡st✐♠❛t✐✈❛s ✐♥❞✐❝❛❞❛s ♥❛ ❚❛❜❡❧❛

      ❆♥❛❧✐s❛♥❞♦ ❛ ❚❛❜❡❧❛ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ s❛í❞❛ ♥❛s ❝❧❛ss❡s ❜♦♥✐✜✲ ❝❛❞❛s ❞♦ s✐st❡♠❛ é ✐♥❢❡r✐♦r às ❞❛s ❝❧❛ss❡s ❛❣r❛✈❛❞❛s✱ ❝♦♠♦ s❡r✐❛ ❡①♣❡❝tá✈❡❧✳ ❆ ♣r♦❜❛✲ ❜✐❧✐❞❛❞❡ ❞❡ s❛í❞❛ ❛✉♠❡♥t❛ ❝♦♠ ♦ ❛❣r❛✈❛♠❡♥t♦ ❛ ❛♣❧✐❝❛r ❛♦ ♣ré♠✐♦ ❛ ♣r✐♦r✐✳ ◆♦t❡✲s❡ q✉❡✱ ♥❛s ❝❧❛ss❡s ❝♦♠ ✶✵✵✪ ❞❡ ❛❣r❛✈❛♠❡♥t♦✱ ❛ t❛①❛ ❞❡ ❛♥✉❧❛çã♦ é ❡❧❡✈❛❞íss✐♠❛✳

      ❚❛❜❡❧❛ ✸✳✼✿ Pr♦❜❛❜✐❧✐❞❛❞❡s ❞❡ ❙❛í❞❛✿ ❙✳ ❆❝t✉❛❧

      2 2

      2 1

      3 2

      3 1

      4 2 ❥ ✶ q (j) 1

      ✵✱✷✷✺✻✻✷ ✵✱✸✼✺✻✺✵ ✵✱✾✺✾✷✸✽ ✵✱✸✼✺✽✸✹ ✵✱✸✼✻✵✷✸ ✵✱✸✽✼✸✶✷

      4

      5

      5

      6

      6 ❥ 1 2 1 2 1 q 1 (j)

      ✵✱✸✽✽✸✵✵ ✵✱✹✹✽✵✺✷ ✵✱✹✹✶✷✷✽ ✵✱✾✶✻✻✻✼ ✵✱✾✺✽✸✸✸ ❆ t❛①❛ ❞❡ ❛♥✉❧❛çã♦ ❞❛ ❈❧❛ss❡ 2 1 ✭❈❧❛ss❡ ❞❡ ❊♥tr❛❞❛✮ é s✉r♣r❡❡♥❞❡♥t❡♠❡♥t❡ ❡❧❡✈❛❞❛✳

      ◆♦ ❡♥t❛♥t♦✱ ❡st❡ ❢❛❝t♦ é ❢❛❝✐❧♠❡♥t❡ ❡①♣❧✐❝á✈❡❧ à ❧✉③ ❞❛ r❡❛❧✐❞❛❞❡ ❡ ❞❛ ❧❡❣✐s❧❛çã♦ ❞❡ ❈❛❜♦ ❱❡r❞❡✿ ❡♥q✉❛♥t♦ ✉♠ ✈❡í❝✉❧♦ s❡ ❡♥❝♦♥tr❛ ♣❛r❛ ✈❡♥❞❛ ♥♦ st❛♥❞ ❞❡ ✈❡♥❞❛s✱ é ♦❜r✐❣❛tór✐❛ ❛ ❝♦♥tr❛t❛çã♦ ❞❡ ✉♠ s❡❣✉r♦ ❞❡ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❝✐✈✐❧ ❛✉t♦♠ó✈❡❧ ♣❛r❛ ❛q✉❡❧❡ ✈❡í❝✉❧♦✳ ◗✉❛♥❞♦ ♦ ✈❡í❝✉❧♦ é ✈❡♥❞✐❞♦✱ ♦ st❛♥❞ ❛♥✉❧❛ ❛ ❛♣ó❧✐❝❡ ❡ s❡rá ❝♦♥tr❛t❛❞❛ ✉♠❛ ♥♦✈❛ ❡♠ ♥♦♠❡ ❞♦ ♥♦✈♦ ♣r♦♣r✐❡tár✐♦✳ ❊st❛ s✐t✉❛çã♦ ❥✉st✐✜❝❛ q✉❡ ❛ t❛①❛ ❞❡ ❛♥✉❧❛çã♦ ♥❛ ♣r✐♠❡✐r❛ ❛♥✉✐❞❛❞❡ ✭♥♦t❡✲s❡ q✉❡✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦✱ ✉♠ s❡❣✉r❛❞♦ só s❡ ♠❛♥té♠ ♥❛ ❈❧❛ss❡ 2 1 ♣♦r ✉♠❛ ❛♥✉✐❞❛❞❡ ❡ ♥ã♦ ♣♦❞❡ ❧á r❡t♦r♥❛r✮ s❡❥❛ ❡①tr❡♠❛♠❡♥t❡ ❡❧❡✈❛❞❛✳

      P❛r❛ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡✱ ❤á ❛✐♥❞❛ q✉❡ ❡st✐♠❛r ❛s ✐♥t❡♥s✐❞❛❞❡s ❞❡

      ✸✳✷ ❙✐st❡♠❛ ❇♦♥✉s ▼❛❧✉s ❆❝t✉❛❧ ❞❛ ●❛r❛♥t✐❛ ✸✼ Pr♦❜❛❜✐❧✐❞❛❞❡s ❞❡ ❈❧❛ss✐✜❝❛çã♦ ■♥✐❝✐❛❧

    • ❈♦♠♦ ❥á ❢♦✐ r❡❢❡r✐❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✐♥✐❝✐❛❧ é ✉♠ ❡❧❡♠❡♥t♦ ✐♠♣♦rt❛♥t❡ ♥❡st❡ ♠♦❞❡❧♦ ❡ ♣❡r♠✐t❡ t❡r ❡♠ ❝♦♥t❛ q✉❡ ♦ s❡❣✉r❛❞♦ ❡stá ✐♥✐❝✐❛❧♠❡♥t❡ s✉❥❡✐t♦ ❛ ✉♠❛ ❝❧❛ss✐✜❝❛çã♦ ♣❛r❛ ♣♦❞❡r s❡r ❝♦❧♦❝❛❞♦ ♥✉♠❛ ❞❛s ❝❧❛ss❡s ❞♦ s✐st❡♠❛✳ ❉❡✈✐❞♦ à ✐♥s✉✜❝✐ê♥❝✐❛ ❞❡ ✐♥❢♦r♠❛çã♦ s♦❜r❡ ❛s ❡♥tr❛❞❛s ♥♦ s✐st❡♠❛ ✭♦s ❞❛❞♦s

      ❞✐s♣♦♥í✈❡✐s r❡❢❡r❡♠✲s❡ ❛♣❡♥❛s ❛ ✸ ❛♥♦s✮✱ ✈❛✐ ❝♦♥s✐❞❡r❛r✲s❡ ❛ ❤✐♣ót❡s❡ ❞♦ ✈❡❝t♦r i ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✐♥✐❝✐❛❧✱ c ✱ s❡r ❝♦♥st❛♥t❡ ❞❡ ❛♥♦ ♣❛r❛ ❛♥♦✱ ♦✉ i 0,j = c , j ∈ C ∪ C 1 2 s❡❥❛✱ ❝♦♥s✐❞❡r❛r✲s❡✲á c ✳ ❆s ❡st✐♠❛t✐✈❛s ♣❛r❛ c ✱ ✐❧✉str❛♠✲s❡

      ♥❛ ❚❛❜❡❧❛ ❆♥❛❧✐s❛♥❞♦ ❛ ❚❛❜❡❧❛ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦s ♥♦✈♦s s❡❣✉r❛❞♦s ♥❡♠ s❡♠♣r❡ ❡♥tr❛♠ ♣❛r❛ ❛ ❝❧❛ss❡ ❞❡ ❡♥tr❛❞❛✱ ♦ q✉❡ r❡✢❡❝t❡ q✉❡ ♦s s❡❣✉r❛❞♦s ♣♦ss❛♠ s❡r s✉❥❡✐t♦s ❛ ✉♠❛ ❝❧❛ss✐✜❝❛çã♦ ✐♥✐❝✐❛❧ q✉❡ ❞❡t❡r♠✐♥❛ ❛ ❝❧❛ss❡ ❞❡ ❜♦♥✉s ♦♥❞❡ ❡st❡s sã♦ ✐♥s❡r✐❞♦s✳ ❊st❡ ❢❛❝t♦ ♣♦❞❡ s❡r ❥✉st✐✜❝❛❞♦✱ ♣r♦✈❛✈❡❧♠❡♥t❡✱ ♣❡❧♦ ✉s♦ ❞♦ ❝❡rt✐✜❝❛❞♦ ❞❡ t❛r✐❢❛çã♦ ♦✉ ♣❡❧♦ ❢❛❝t♦ ❞❡ ♦ ♠❡r❝❛❞♦ s❡❣✉r❛❞♦r✱ ❡♠ ❈❛❜♦ ❱❡r❞❡✱ ♥ã♦ s❡r ♠✉✐t♦ ❝♦♥❝♦rr❡♥❝✐❛❧✳ ◆♦t❡✲s❡ q✉❡✱ ♥❛ r❡❛❧✐❞❛❞❡✱ ♦s ♥♦✈♦s s❡❣✉r❛❞♦s ♣♦❞❡♠ ♥ã♦ s❡r ✐♥s❡r✐❞♦s ♥❛ ❝❧❛ss❡ ❞❡ ❡♥tr❛❞❛ ♣♦r ❞✐✈❡rs♦s ♠♦t✐✈♦s✳

      ❚❛❜❡❧❛ ✸✳✽✿ Pr♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ❈❧❛ss✐✜❝❛çã♦ ■♥✐❝✐❛❧✿ ❙✳ ❆❝t✉❛❧

      2

      2

      3

      3

      4 ❥ ✶ 2 1 2 1 2 c

    0,j ✵✱✵✽✼✵✾✸✽ ✵✱✵✶✺✻✹✺✸ ✵✱✽✽✼✵✵✶ ✵✱✵✵✹✶✸✶✽✺ ✵✱✵✵✹✶✸✶✽✺ ✵✱✵✵✵✽✸✺✻✺✺

      4

      5

      5

      6

      6 ❥ 1 2 1 2 1 c 0,j ✵✱✵✵✵✼✹✷✽✵✹ ✵✱✵✵✵✶✸✾✷✼✻ ✵✱✵✵✵✵✹✻✹✷✺✸ ✵✱✵✵✵✶✸✾✷✼✻ ✵✱✵✵✵✵✾✷✽✺✵✺

      ❆s ❊♥tr❛❞❛s ♥♦ ❙✐st❡♠❛

    • ❖ ♥ú♠❡r♦ ❞❡ ♥♦✈❛s ❡♥tr❛❞❛s ❞❡ ❛♣ó❧✐❝❡s ♥♦ s✐st❡♠❛✱ ❞♦ ❛♥♦ ✶✾✾✾ ❛ ✷✵✵✾✱ ♣♦❞❡ ❝♦♥s✉❧t❛r✲s❡ ♥❛ ❚❛❜❡❧❛ q✉❡ ♥ã♦ ❝♦rr❡s♣♦♥❞❡rá ❛♣❡♥❛s ❛♦ ♥ú♠❡r♦ ❞❡ ♥♦✈❛s ❛♣ó❧✐❝❡s ✈❡♥❞✐❞❛s ♥❡ss❡ ❛♥♦✳ Pr❡t❡♥❞❡✲s❡ ❛❥✉st❛r ✉♠ ♠♦❞❡❧♦ ♣❛r❛ ♦ ✢✉①♦ ❞❡ ♥♦✈❛s ❡♥tr❛❞❛s ♥♦ s✐st❡♠❛✳ ❈♦♥✲

      s✐❞❡r♦✉✲s❡ ✉♠ ♠♦❞❡❧♦ ❡♠ q✉❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❡✈♦❧✉çã♦ ❞❛s ♥♦✈❛s ❛♣ó❧✐❝❡s é ❛ss✐♠♣tót✐❝♦✳ ❚r❛t❛✲s❡ ❞♦ ♠♦❞❡❧♦ q✉❡ ♣❛r❡❝❡ s❡r ♠❛✐s ♣❧❛✉sí✈❡❧ ❛❥✉st❛r ♣♦✐s ❛❞❡q✉❛✲s❡ à r❡❛❧✐❞❛❞❡ ❞♦ ♠❡r❝❛❞♦ s❡❣✉r❛❞♦r✿ ❛ s❡❣✉r❛❞♦r❛ t❡♠ ❝♦♠♦ ♦❜❥❡❝t✐✈♦ ♦ ❝r❡s❝✐♠❡♥t♦ ❞♦ s❡✉ ♥❡❣ó❝✐♦✱ ♦ q✉❡ ❛❥✉st❛r✲s❡✲á✱ ❛♦s ❞❛❞♦s ❞❡ ❡♥tr❛❞❛s ❞❡ ♥♦✈❛s i = τ (1 − e ), i ∈ N, τ > 0, δ > 0 − δi

      ✸✽ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❚❛❜❡❧❛ ✸✳✾✿ ❊♥tr❛❞❛s ❞❡ ◆♦✈❛s ❆♣ó❧✐❝❡s

      ❆♥♦ ◆✳

      ♦

      ❞❡ ◆♦✈❛s ❆♣ó❧✐❝❡s ✶✾✾✽ ✽✻✼✽ ✶✾✾✾ ✷✾✹✾ ✷✵✵✵ ✷✽✺✶ ✷✵✵✶ ✷✷✹✵ ✷✵✵✷ ✷✼✼✶ ✷✵✵✸ ✸✹✷✸ ✷✵✵✹ ✹✸✵✻ ✷✵✵✺ ✹✼✺✸ ✷✵✵✻ ✺✷✸✾ ✷✵✵✼ ✻✾✵✸ ✷✵✵✽ ✼✹✹✾ ✷✵✵✾ ✼✶✽✽

      ❖ ❡st✐♠❛❞♦r ❞❡ ♠á①✐♠❛ ✈❡r♦s✐♠✐❧❤❛♥ç❛ ♣❛r❛ τ✱ ✈❡r s❡rá ❞❛❞♦ ♣♦r

      ˆ τ = N • ,• P m i=1 (1 − e −ˆ δi )

      ✭✸✳✶✽✮ ❡ ˆδ✱ ❡st✐♠❛❞♦r ❞❡ ♠á①✐♠❛ ✈❡r♦s✐♠✐❧❤❛♥ç❛ ♣❛r❛ δ✱ s❡rá ❞❛❞♦ ♣❡❧❛ s♦❧✉çã♦ ❞❛ ❡q✉❛çã♦

      − N • ,• P m i=1

      (1 − e δi ) m X i=1 ie − δi + m X i=1 ie − δi 1 − e δi N i,• = 0

      ✭✸✳✶✾✮ ❝♦♠

       N • ,j = P m i=1 N i,j N i,• = P s j=1 N i,j N • ,• = P m i=1 P s j=1 N i,j , .

      ✭✸✳✷✵✮ ❊st✐♠❛♥❞♦ ♦s ♣❛râ♠❡tr♦s✱ ♦❜t❡✈❡✲s❡ ˆτ = 7736 ❡ ˆδ = 0, 171864944✱ ♦ q✉❡ s❡ tr❛❞✉③✐rá ❡♠✿

      ˆ λ i = 7736(1 − e − 0,171864944i ), i ∈ N.

      ✭✸✳✷✶✮ P❛r❛ ♦ ❛❥✉st❛♠❡♥t♦ ❡❢❡❝t✉❛❞♦✱ ♦❜t❡✈❡✲s❡ R 2

      = 0, 71019519 ❡ ♦ ❣rá✜❝♦ ♣♦❞❡ s❡r

      ❛♥❛❧✐s❛❞♦ ♥❛ ❋✐❣✉r❛ ❆♥❛❧✐s❛♥❞♦ ❛ ❋✐❣✉r❛ ✈❡r✐✜❝❛✲s❡ q✉❡✱ ❛ q✉❛❧✐❞❛❞❡ ❞♦ ❛❥✉st❛♠❡♥t♦ ♥ã♦ é ❛ ♠❡❧❤♦r✱

      ✸✳✷ ❙✐st❡♠❛ ❇♦♥✉s ▼❛❧✉s ❆❝t✉❛❧ ❞❛ ●❛r❛♥t✐❛ ✸✾ ❋✐❣✉r❛ ✸✳✷✿ ❆❥✉st❛♠❡♥t♦ ❛ss✐♠♣tót✐❝♦ às ❊♥tr❛❞❛s ♥♦ ❙✐st❡♠❛

      3 1 ✵✱✵✸✶✶✸✸✾✻

      6 1 ✵✱✵✵✵✷✹✵✻✸ ❚♦t❛❧ ✶

      6 2 ✵✱✵✵✵✶✵✶✷✺

      5 1 ✵✱✵✵✵✽✾✵✹✺

      5 2 ✵✱✵✵✵✸✺✽✽✸

      4 1 ✵✱✵✵✺✷✷✸✽✽

      4 2 ✵✱✵✵✷✺✽✸✾✶

      3 2 ✵✱✵✶✼✹✺✻✹✸

      ❤á ✉♠❛ ❡st❛❜✐❧✐③❛çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ♥♦✈❛s ❡♥tr❛❞❛s ♥♦ s✐st❡♠❛✳ ❉❛ ❡q✉❛çã♦ ✐♥❢❡r❡✲s❡ q✉❡ r❡❧❛t✐✈❛♠❡♥t❡ à ♠♦❞❡❧❛çã♦ ♦r✐❣✐♥❛❧ ❞❡

      2 1 ✵✱✻✵✽✹✺✵✽✵

      2 2 ✵✱✵✸✷✹✻✹✼✸

      ❚❛❜❡❧❛ ✸✳✶✵✿ ❉✐str✐❜✉✐çã♦ ▲✐♠✐t❡ ✭▼♦❞❡❧♦ ❆❜❡rt♦✮✿ ❙✳ ❆❝t✉❛❧ j π T ✶ ✵✱✸✵✶✵✾✺✶✸

      θ = e −ˆ δ = e − 0,171864944 = 0, 842092895, ✈❡r✐✜❝❛♥❞♦✲s❡ ♣♦rt❛♥t♦ 0 < θ < 1✱ ♦✉ s❡❥❛✱ ❣❛r❛♥t❡✲s❡ ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ✈órt✐❝❡ ❡st♦❝ást✐❝♦ ♥♦ SBM✱ ♦ q✉❡ tr❛❞✉③ ♥❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡✱ q✉❡ ♣♦❞❡rá ❢❛❝✐❧♠❡♥t❡ s❡r ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❡

      ❡ ˆ

      λ i = a + bθ i , (a, b, θ) ∈ Θ, i ∈ N t❡♠✲s❡ q✉❡ ˆ a = −ˆb = 7736

      ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ ♣❛r❛ ✉♠ s❡❣✉r❛❞♦ r❡t✐r❛❞♦ ❛♦ ❛❝❛s♦ ❞❛

      ✹✵ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ 1 ❣r❛♥❞❡ ❛❣❧♦♠❡r❛çã♦ ❞❡ ❛♣ó❧✐❝❡s ♥❛ ❝❧❛ss❡ ❞❡ ❡♥tr❛❞❛ ✭❈❧❛ss❡ 2 ✮✳ ❖ ♣ré♠✐♦ ♠é❞✐♦✱ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ é ✾✷✱✵✷✪ ❞♦ ♣ré♠✐♦ ❞❡ ❡♥tr❛❞❛✳

      ❋✐❣✉r❛ ✸✳✸✿ ❊✈♦❧✉çã♦ ❞♦ Pré♠✐♦ ▼é❞✐♦ ✲ ▼♦❞❡❧♦ ❆❜❡rt♦✿ ❙✳ ❆❝t✉❛❧ ❆ ❋✐❣✉r❛ ✐❧✉str❛ ❛ ❡✈♦❧✉çã♦ ❞♦ ♣ré♠✐♦ ♠é❞✐♦ ❞❡ ✉♠ ♥♦✈♦ s❡❣✉r❛❞♦ r❡t✐r❛❞♦ ❛♦

      ❛❝❛s♦✱ ♥♦ ❞❡❝♦rr❡r ❞♦s ♣ró①✐♠♦s ✷✵ ❛♥♦s✱ ❡♠ ♣❡r❝❡♥t❛❣❡♠ ❞♦ ♣ré♠✐♦ ❞❡ ❡♥tr❛❞❛✳ ❆♥❛❧✐s❛♥❞♦ ❛ ❋✐❣✉r❛ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦ ♣ré♠✐♦ ♠é❞✐♦ ❞✐♠✐♥✉✐ ❛♦ ❧♦♥❣♦ ❞♦s ❛♥♦s✱

      ♦

      só ❡st❛❜✐❧✐③❛♥❞♦ ❛ ♣❛rt✐r ❞♦ ✶✺ ❛♥♦✳ ❆♦ ✜♠ ❞❡ ✷✵ ❛♥♦s✱ ♦ ♣ré♠✐♦ ♠é❞✐♦ ❡♥❝♦♥tr❛✲s❡ ♣ró①✐♠♦ ❞♦ ✈❛❧♦r ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ❡♠❜♦r❛ ❡st❛ só s❡❥❛ ❡❢❡❝t✐✈❛♠❡♥t❡ ❛t✐♥❣✐❞❛ ❛♣ós ✹✼ ❛♥✉✐❞❛❞❡s✳

      ❆ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ ♦❜t✐❞❛ ❛tr❛✈és ❞❡st❡ ♠♦❞❡❧♦ é s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ❞✐❢❡r❡♥t❡ ❞❛ ♦❜t✐❞❛ ♣❡❧♦ ♠♦❞❡❧♦ ❝❧áss✐❝♦✳ ❊♥q✉❛♥t♦ q✉❡ ♥♦ ♠♦❞❡❧♦ ✈órt✐❝❡s ❡st♦❝ást✐❝♦s✱ ♥❛ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ❡①✐st✐rá ✉♠❛ ❣r❛♥❞❡ ❛❣❧♦♠❡r❛çã♦ ❞❡ ❛♣ó❧✐❝❡s ♥❛ ❝❧❛ss❡ ❞❡ ❡♥tr❛❞❛✱ ♥♦ ♠♦❞❡❧♦ ❝❧áss✐❝♦✱ ❛ ♠❛✐♦r ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❛♣ó❧✐❝❡s s❡rá ♥❛ ❝❧❛ss❡ ❜♦♥✐✜❝❛❞❛✳ ❊♠ ❛♠❜♦s ♦s ♠♦❞❡❧♦s✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ♠❛✐♦r ♣❛rt❡ ❞❛s ❛♣ó❧✐❝❡s ❡♥❝♦♥tr❛r✲s❡✲ã♦ ♥❛s ❝❧❛ss❡s 1

      ♥ã♦ ❛❣r❛✈❛❞❛s ✭❈❧❛ss❡ ✶ ❡ ❈❧❛ss❡ 2 ✮✱ s❡♥❞♦ q✉❡✱ ♥♦ ♠♦❞❡❧♦ ✈órt✐❝❡s ❡st♦❝ást✐❝♦s ❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❛♣ó❧✐❝❡s ♥❛s ❝❧❛ss❡s ♥ã♦ ❛❣r❛✈❛❞❛s s❡rá ❛✐♥❞❛ ♠❛✐♦r✳ ❊st❡ ❢❛❝t♦ é r❡✢❡①♦ ❞❛s ❡❧❡✈❛❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ s❛í❞❛ ♥❛s ❝❧❛ss❡s ♠❛✐s ❛❣r❛✈❛❞❛s✱ q✉❡ ♥ã♦ sã♦ t✐❞❛s ❡♠ ❝♦♥t❛ ♥♦ ♠♦❞❡❧♦ tr❛❞✐❝✐♦♥❛❧✳ ❱❡r✐✜❝❛✲s❡ ❛✐♥❞❛ q✉❡✱ ❡♠ ❛♠❜♦s ♦s ♠♦❞❡❧♦s✱ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡✱ ♥❛ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ✉♠❛ ❛♣ó❧✐❝❡ s❡ ❡♥❝♦♥tr❛r ♥❛ ❝❧❛ss❡ ❝♦♠ ♦ ♠❡s♠♦ ❛❣r❛✈❛♠❡♥t♦ ♣❡❧♦ s❡❣✉♥❞♦ ❛♥♦ ❝♦♥s❡❝✉t✐✈♦ ❞✐♠✐♥✉✐✳ ❊st❡ ❢❛❝t♦ ♣♦❞❡ ❥✉st✐✜❝❛r✲s❡ ♣❡❧❛s ❛❝t✉❛✐s r❡❣r❛s ❞❡ tr❛♥s✐çã♦✱ ✈✐st♦ q✉❡ é ♠❛✐s ✈❛♥t❛❥♦s♦ ♣❛r❛ ♦ s❡❣✉r❛❞♦ ♥ã♦ ❝♦♥t✐♥✉❛r ♥❛ ❝❧❛ss❡ ❝♦♠ ♦ ♠❡s♠♦ ❛❣r❛✈❛♠❡♥t♦ ♣❡❧♦ s❡❣✉♥❞♦ ❛♥♦ ❝♦♥s❡❝✉t✐✈♦✳

      ✸✳✷✳✹ ❊s❝❛❧❛s Ó♣t✐♠❛s

      ❖ ▼♦❞❡❧♦ ❞❡ ◆♦r❜❡r❣ ❆ ❡s❝❛❧❛ ó♣t✐♠❛ ❞❡ ♣ré♠✐♦s✱ ♦❜t✐❞❛ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ❞❡ ❛♣r❡s❡♥t❛❞♦ ♥❛ ❙✉❜✲s❡❝çã♦ é ❞❛❞❛ ♣♦r✿ R b (j) = , j ∈ C ∪ C . T 1 2

      ✭✸✳✷✷✮

      ✸✳✷ ❙✐st❡♠❛ ❇♦♥✉s ▼❛❧✉s ❆❝t✉❛❧ ❞❛ ●❛r❛♥t✐❛ ✹✶ ◆♦t❡✲s❡ q✉❡ ❛ ❡s❝❛❧❛ ❞❡ ❡st✐♠❛rá ♦ ♣ré♠✐♦ ó♣t✐♠♦ ❛ ❛♣❧✐❝❛r ❛ ❝❛❞❛ ❝❧❛ss❡✱ s❡♠ t❡r ❡♠ ❝♦♥t❛ q✉❡✱ ❞❡✈✐❞♦ ❛♦ ❞❡s❞♦❜r❛♠❡♥t♦ ❞❛s ❝❧❛ss❡s q✉❡ ❢♦✐ ♥❡❝❡ssár✐♦

      , j = 2, . . . , 6 ❡❢❡❝t✉❛r✱ ♦s ♣ré♠✐♦s ❞❛s ❝❧❛ss❡s j 1 ❡ j 2 ❞❡✈❡rã♦ s❡r ✐❣✉❛✐s✳

      P❛r❛ q✉❡ ❛ ❡s❝❛❧❛ ❞❡ ♣ré♠✐♦s ♦❜t✐❞❛ ❛tr❛✈és ❞❡st❡ ♠♦❞❡❧♦ r❡s♣❡✐t❡ ❛ ❞❡✜♥✐çã♦ ❞♦ SBM

      ✉t✐❧✐③❛❞♦ ♥❡st❛ s❡❣✉r❛❞♦r❛✱ ❡ s❡❣✉✐♥❞♦ ❛ s✉❣❡stã♦ ❞❡ ❛ ❡s❝❛❧❛ ❞❡ s♦❜ ❛ r❡str✐çã♦ ❞❛ ✐❣✉❛❧❞❛❞❡ ❞❡ ♣ré♠✐♦s ❡♠ ❝❧❛ss❡s ❞❡s❞♦✲ ❜r❛❞❛s é ❞❛❞❛ ♣♦r✿ P 2 ∗ l=1 ∗ b T (j )π T (j ) l l b (j) = , j = 2, . . . , 6, (1) = b T (1). T P ❡ b T ✭✸✳✷✸✮ 2 l=1 π T (j ) l

      ❯t✐❧✐③❛♥❞♦ ❛s ❞✐str✐❜✉✐çõ❡s ❧✐♠✐t❡ ♦❜t✐❞❛s ♥❛s ❚❛❜❡❧❛s ❛s ❡s❝❛❧❛s ó♣t✐♠❛s ❞❡ ♣ré♠✐♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ❡ ❛❜❡rt♦✱ ♣♦❞❡♠ s❡r ❝♦♥s✉❧t❛❞❛s ♥❛ ❚❛❜❡❧❛

      ❚❛❜❡❧❛ ✸✳✶✶✿ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s ✭▼♦❞❡❧♦ ❞❡ ❙✳ ❆❝t✉❛❧ b T (j) ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ▼♦❞❡❧♦ ❆❜❡rt♦

      ✶ ✵✱✵✽✽✼✺✼✽ ✵✱✶✵✵✵✹✻✷ ✷ ✲ ✵✱✶✺✵✸✽✾✾ ✸ ✵✱✸✷✼✺✹✶✹ ✵✱✷✽✽✸✹✽✼ ✹ ✵✱✺✸✼✾✽✹✸ ✵✱✹✺✾✵✻✼✽ ✺ ✵✱✻✽✽✷✺✶✷ ✵✱✻✶✾✸✽✵✺ ✻ ✵✱✼✾✽✺✺✷✼ ✵✱✺✸✾✷✽✷✽

      ❆♥❛❧✐s❛♥❞♦ ❛s ❡s❝❛❧❛s ❞❡ ♣ré♠✐♦s ♦❜t✐❞❛s✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ♥❛s ❝❧❛ss❡s ♥ã♦ ❛❣r❛✈❛❞❛s ✭❈❧❛ss❡s ✶ ❡ ✷✮ ♦ ♣ré♠✐♦ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ é ✐♥❢❡r✐♦r ❛♦ ♣ré♠✐♦ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ ❡♥q✉❛♥t♦ q✉❡ ♥❛s ❝❧❛ss❡s ❛❣r❛✈❛❞❛s ✭❞❛ ❈❧❛ss❡ ✸ à ❈❧❛ss❡ ✻✮ ♦ ♣ré♠✐♦ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ é s✉♣❡r✐♦r ❛♦ ♣ré♠✐♦ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦✳ ❱❡r✐✜❝❛✲s❡ ❛✐♥❞❛ q✉❡ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦ ❛ ❡s❝❛❧❛ ♦❜t✐❞❛ ♥ã♦ ❝r❡s❝❡ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ♣r♦♣❡♥sã♦ à s✐♥✐str❛❧✐❞❛❞❡❀ ❤á ✉♠❛ q✉❡❜r❛ ❞♦ ♣ré♠✐♦ ♥❛ ❝❧❛ss❡ ♠❛✐s ❛❣r❛✈❛❞❛ ✭❈❧❛ss❡ ✻✮✳ ❊st❡ ❢❛❝t♦ ❞❡✈❡✲s❡✱ ♣♦ss✐✈❡❧♠❡♥t❡✱ às ❛❝t✉❛✐s r❡❣r❛s ❞❡ tr❛♥s✐çã♦ ❞♦ s✐st❡♠❛ ❡ às ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ s❛í❞❛✳ T (2 1 ) = π T (2 2 ) = 0

      ◆♦t❡✲s❡ q✉❡✱ ✉♠❛ ✈❡③ q✉❡ π ✱ ❛ ❡①♣r❡ssã♦ ♥ã♦ ♣❡r♠✐t✐rá ❡st✐♠❛r ♦ ♣ré♠✐♦ ❞❛ ❈❧❛ss❡ ✷ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✳

      ❈♦♠♦ ♦ ❝✉st♦ ♠é❞✐♦ ❞❡ ✉♠ s✐♥✐str♦ é ❝♦♥s✐❞❡r❛❞♦ ✉♥✐tár✐♦✱ ♦ ♣ré♠✐♦ ❛ ❝♦❜r❛r ❝♦rr❡s♣♦♥❞❡ ❛♣❡♥❛s à ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ ❞❡ ❝❛❞❛ ❝❧❛ss❡✳ ❆ss✐♠✱ s❡♥❞♦ ❛ ❈❧❛ss❡ T (2) ✷ ❛ ❝❧❛ss❡ ❞❡ ❡♥tr❛❞❛ ♣♦❞❡r✲s❡✲á ♦♣t❛r ♣♦r ✉s❛r ❝♦♠♦ ❡st✐♠❛t✐✈❛ ❞❡ b ✱ ❛ ❢r❡q✉ê♥❝✐❛ T (2) = ˆ λ = 0, 1475536 ❞❡ s✐♥✐str❛❧✐❞❛❞❡ ♠é❞✐❛ ❞❛ ❝❛rt❡✐r❛✱ ♦✉ s❡❥❛ b ✳ ❖✉tr❛ s✉❣❡stã♦✱ ♠❛✐s ❛❞❡q✉❛❞❛ ❞♦ ♥♦ss♦ ♣♦♥t♦ ❞❡ ✈✐st❛✱ s❡rá ❛ ❡st✐♠❛çã♦ ❞❛ ❡s❝❛❧❛ ó♣t✐♠❛ ❞❡ ♣ré♠✐♦s r❡❝♦rr❡♥❞♦ ❛♦ ♠♦❞❡❧♦ ❞❡ ❝♦♥❢♦r♠❡ s❡ ❢❛rá ❛❞✐❛♥t❡✳

      ◆❛ ❚❛❜❡❧❛ ♣♦❞❡♠ s❡r ❝♦♥s✉❧t❛❞♦s ♦ ♣ré♠✐♦ ♠é❞✐♦ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛✲ r✐❞❛❞❡✱ ♦ ❡rr♦ q✉❛❞rát✐❝♦ ♠é❞✐♦ ❡ ❛ ♠❡❞✐❞❛ ❞❡ ❡✜❝✐ê♥❝✐❛ ♣❛r❛ ♦s ❞♦✐s ♠♦❞❡❧♦s✳ ❖ ♣ré♠✐♦ ♠é❞✐♦ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦ é ❧✐❣❡✐r❛♠❡♥t❡

      ✹✷ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❚❛❜❡❧❛ ✸✳✶✷✿ P M✱ EQM ❡ ▼❡❞✐❞❛ ❞❡ ❊✜❝✐ê♥❝✐❛ ✭▼♦❞❡❧♦ ❞❡ ❙✳ ❆❝t✉❛❧

      ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ▼♦❞❡❧♦ ❆❜❡rt♦ P M

      ✵✱✶✹✺✵✺✸✼ ✵✱✶✹✺✵✻✹✶ EQM

      ✵✱✵✷✽✹✶✾✻ ✵✱✵✸✾✾✽✾ e(∆) ✵✱✵✸✺✸✷✽✸ ✵✱✵✷✸✼✼✸✻

      ❡①✐st✐r ♠❛✐s s❡❣✉r❛❞♦s ♥❛ ❝❧❛ss❡ ❜♦♥✐✜❝❛❞❛ ❞♦ s✐st❡♠❛ ❛ ❧♦♥❣♦ ♣r❛③♦✳ ❆s ♠❡❞✐❞❛s ❛♣r❡s❡♥t❛❞❛s ♥❛ ❚❛❜❡❧❛ ♥ã♦ ❞❡✈❡♠ s❡r ❝♦♠♣❛r❛❞❛s ❡♥tr❡ s✐✱ ✉♠❛

      ✈❡③ q✉❡ ❞❡✈❡rã♦ ❛♣❡♥❛s s❡r ✉t✐❧✐③❛❞❛s ♣❛r❛ ❝♦♠♣❛r❛r ❛ ❡✜❝✐ê♥❝✐❛ ❞❡ ❞✐❢❡r❡♥t❡s ❡s❝❛❧❛s ó♣t✐♠❛s ❝❛❧❝✉❧❛❞❛s ♣❛r❛ ♦ ♠❡s♠♦ SBM✱ ✉t✐❧✐③❛♥❞♦ ♦s ♠❡s♠♦s ♣r❡ss✉♣♦st♦s✳ ❙❡rã♦✱ ♣♦rt❛♥t♦✱ út❡✐s ♥❛s ❝♦♠♣❛r❛çõ❡s ❢❡✐t❛s ❛❞✐❛♥t❡ ❛♣ós ❛ ❡st✐♠❛çã♦ ❞❡ ♦✉tr❛s ❡s❝❛❧❛s ó♣t✐♠❛s s♦❜ ❝❛❞❛ ✉♠❛ ❞❛s ♣❡rs♣❡❝t✐✈❛s✳

      ◆❛ ❋✐❣✉r❛ ♣♦❞❡ s❡r ❛♥❛❧✐s❛❞❛ ❛ ❡✈♦❧✉çã♦ ❞♦ ♣ré♠✐♦ ♠é❞✐♦ ❞❡ ✉♠ ♥♦✈♦ s❡❣✉r❛❞♦ r❡t✐r❛❞♦ ❛♦ ❛❝❛s♦ ❞❛ ❝❛rt❡✐r❛ ❞❡ ❛♣ó❧✐❝❡s✱ ♣❛r❛ ♦s ♣ró①✐♠♦s ✷✵ ❛♥♦s✳ ❋✐❣✉r❛ ✸✳✹✿ ❊✈♦❧✉çã♦ ❞♦ Pré♠✐♦ ▼é❞✐♦ ✭❊s❝❛❧❛ ❞❡ ❙✐st❡♠❛ ❆❝t✉❛❧

      ❆♥❛❧✐s❛♥❞♦ ❛ ❋✐❣✉r❛ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦ ♣ré♠✐♦ ♠é❞✐♦✱ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✱ ❡st❛❜✐✲

      ♦

      ❧✐③❛ ❧♦❣♦ ♥♦ ✷ ❛♥♦✱ ✜❝❛♥❞♦✲s❡ ♠✉✐t♦ ♣ró①✐♠♦ ❞❛ ❡st❛❝✐♦♥❛r✐❞❛❞❡✳ ◆♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱

      ♦

      ♦ ♣ré♠✐♦ ♠é❞✐♦ ✈❛✐ ❞✐♠✐♥✉✐♥❞♦ ♥♦ ❞❡❝♦rr❡r ❞♦s ❛♥♦s✱ ❡ ❡st❛❜✐❧✐③❛ ❛ ♣❛rt✐r ❞♦ ✶✺ ❛♥♦✱ s❡♥❞♦ q✉❡ ♦ ♣ré♠✐♦ ♠é❞✐♦✱ ♣❛ss❛❞♦s ✷✵ ❛♥♦s✱ ❡♥❝♦♥tr❛✲s❡ ♠✉✐t♦ ♣ró①✐♠♦ ❞❛ ❡st❛❝✐♦♥❛r✲ ✐❞❛❞❡✳ ◆♦ ♣r✐♠❡✐r♦ ❛♥♦✱ ♦ ♣ré♠✐♦ ♠é❞✐♦ ❞❡ ✉♠ ♥♦✈♦ s❡❣✉r❛❞♦ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ❡ ❛❜❡rt♦ sã♦ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ✵✱✶✼✹✶✷✶✻✶✼ ❡ ✵✱✶✹✼✽✵✾✼✸✸✳ ❖♣t♦✉✲s❡ ♣♦r ♥ã♦ ✐❧✉str❛r ♦ ♣ré♠✐♦ ♠é❞✐♦ ♥♦ ♣r✐♠❡✐r♦ ❛♥♦ ♣♦rq✉❡✱ ♦ ♣ré♠✐♦ ♦❜t✐❞♦ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ♥❡ss❡ ❛♥♦ é s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ s✉♣❡r✐♦r ❛♦s ♦✉tr♦s ♣ré♠✐♦s ♦❜t✐❞♦s✱ ♦ q✉❡ ♥ã♦ ♣❡r♠✐t✐❛ ❛♥❛❧✐s❛r ❞❡ ❢♦r♠❛ ❝❧❛r❛ ❛ ❡✈♦❧✉çã♦ ❞♦s ♣ré♠✐♦s ♥♦s ❛♥♦s s❡❣✉✐♥t❡s✳ ❖ ▼♦❞❡❧♦ ❞❡ ❇♦r❣❛♥✱ ❍♦❡♠ ✫ ◆♦r❜❡r❣ ❙❡❣✉✐♥❞♦ ❛ s✉❣❡stã♦ ❛♣r❡s❡♥t❛❞❛ ♣♦r ❝♦♥s✐❞❡r♦✉✲s❡ ✜①♦ ✉♠

      ✸✳✷ ❙✐st❡♠❛ ❇♦♥✉s ▼❛❧✉s ❆❝t✉❛❧ ❞❛ ●❛r❛♥t✐❛ ✹✸ ♣ré♠✐♦ ♠é❞✐♦ ❡st❛❜✐❧✐③❛ ❧♦❣♦ ♥♦ ✷

      ▼✳ ❋❡❝❤❛❞♦ ▼✳ ❆❜❡rt♦ ✶ ✵✱✺✽✸✻✼✾✷✸✾ ✵✱✷✹✹✺✵✹✾✵✹

      6 2 ✵✱✵✵✵✷✷✾✾✹✺ ✵✱✵✵✵✶✶✵✽✵✻

      5 1 ✵✱✵✵✸✷✽✵✼✻✷ ✵✱✵✵✵✼✷✹✵✽✼

      5 2 ✵✱✵✵✶✷✶✽✼✽✶ ✵✱✵✵✵✸✵✵✺✶✽

      4 1 ✵✱✵✶✼✸✹✼✽✶✼ ✵✱✵✵✹✸✵✽✶✷✹

      4 2 ✵✱✵✵✼✹✽✽✾✼✽ ✵✱✵✵✷✶✹✺✹✵✽

      3 1 ✵✱✵✾✼✻✶✽✵✺✷ ✵✱✵✷✺✶✾✵✸✽✼

      3 2 ✵✱✵✺✶✽✵✻✵✼✺ ✵✱✵✶✸✽✵✽✾✻✽

      2 1 ✵ ✵✱✻✼✺✹✵✵✻✾

      2 2 ✵✱✷✸✻✻✸✼✻✺✷ ✵✱✵✸✸✷✾✷✺✻✻

      ✭✸✳✷✻✮ ❚❛❜❡❧❛ ✸✳✶✸✿ ❉✐str✐❜✉✐çã♦ P♦♥❞❡r❛❞❛✿ ❙✐st❡♠❛ ❆❝t✉❛❧ p ∆ (j l )

      ♦

      ❡ p (j) = #n X n=1 w n Z p (n) ∆,λ (j)dU (λ), j ∈ C 1 ∪ C 2 .

      , j ∈ C 1 ∪ C 2 ✭✸✳✷✺✮

      ✭✸✳✷✹✮ ♦♥❞❡ b B (j) = P #n n=1 w n R E(S n |λ)p (n) ∆,λ (j)dU (λ) p (j)

      ❡ b B (1) = b B (1)

      (j l ) , j = 2, . . . , 6

      ❈♦♥s✐❞❡r❛♥❞♦ ♦ ❞❡s❞♦❜r❛♠❡♥t♦ ❞❛s ❝❧❛ss❡s ❞❡ ❜♦♥✉s✱ ❛ ❡s❝❛❧❛ ❞❡ s❡rá ❞❛❞❛ ♣♦r✿ b B (j) = P 2 l=1 b B (j l )p (j l ) P 2 l=1 p

      ❊♠ r❡❧❛çã♦ ❛♦ ♣❡s♦ ❛ ❛tr✐❜✉✐r à ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ♦♣t♦✉✲s❡ ♣♦r ♥ã♦ ❞❡t❡r♠✐♥❛r ♥❡♥✲ ❤✉♠ ✈❛❧♦r ❛ ♣r✐♦r✐✱ ❞❡✐①❛♥❞♦ q✉❡ ♦ ♣❡s♦ s❡❥❛ ❛tr✐❜✉í❞♦ ♣❡❧❛ ❝♦♥✈❡r❣ê♥❝✐❛ ♣❛r❛ ❛ ❡st❛❝✐♦✲ ♥❛r✐❞❛❞❡ ❞♦ ♣ró♣r✐♦ s✐st❡♠❛✳ ❈❛s♦ ♦ s✐st❡♠❛ ♥ã♦ ❛t✐♥❥❛ ❛ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ❝♦♥s✐❞❡r❛✲ s❡ q✉❡ ♦ ♣❡s♦ ❛ ❛tr✐❜✉✐r à ❡st❛❝✐♦♥❛r✐❞❛❞❡ ❞❡✈❡ s❡r ♥✉❧♦✳ ◆❛ r❡s♦❧✉çã♦ ❞♦ s✐st❡♠❛✱ ❝♦♥s✐❞❡r♦✉✲s❡ i✱ ✜①♦✱ ✐❣✉❛❧ ❛ ✺✪✱ ❝♦♥❢♦r♠❡ ✉t✐❧✐③❛❞♦ ♣❡❧♦s ♠❡s♠♦s ❛✉t♦r❡s✳

      ♦♥❞❡ #n ❝♦rr❡s♣♦♥❞❡ ❛♦ ♥ú♠❡r♦ ❞❡ ♣♦♥❞❡r❛❞♦r❡s ❛ ❝♦♥s✐❞❡r❛r ❡ i ♣❡r♠✐t❡ ❡st❛❜❡❧❡❝❡r ❛ r❡❧❛çã♦ ❡♥tr❡ ♦s ♣♦♥❞❡r❛❞♦r❡s ♣❛r❛ ❝❛❞❛ ❛♥♦✳

      ❛♥♦✱ ✜❝❛♥❞♦ ♠✉✐t♦ ♣ró①✐♠♦ ❞♦ ♣ré♠✐♦ ❞❡ ❡st❛✲ ❝✐♦♥❛r✐❞❛❞❡✱ ❝♦♥s✐❞❡r♦✉✲s❡ ❛♣❡♥❛s ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✹ ♣♦♥❞❡r❛❞♦r❡s✱ ❛♠❜♦s ♦s ❝♦♥❥✉♥t♦s ❞❡t❡r♠✐♥❛❞♦s ❛tr❛✈és ❞♦ s✐st❡♠❛ ❞❡ ❡q✉❛çõ❡s✿ w P n = w n −1 1+i #n n=1 w n = 1

      6 1 ✵✱✵✵✵✻✾✷✻✾✽ ✵✱✵✵✵✷✶✸✺✹✹

      ✹✹ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❆ ❡①♣r❡ssã♦ é ❞❡s✐❣♥❛❞❛ ♣♦r ❞✐str✐❜✉✐çã♦ ♣♦♥❞❡r❛❞❛ ❡ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s

      ♣❛r❛ ❝❛❞❛ ✉♠ ❞♦s ❝♦♥❥✉♥t♦s ♣♦❞❡♠ s❡r ❝♦♥s✉❧t❛❞❛s ♥❛ ❚❛❜❡❧❛ ❆♥❛❧✐s❛♥❞♦ ❛ ❚❛❜❡❧❛ ❡ ❝♦♠♣❛r❛♥❞♦ ❝♦♠ ❛s ❞✐str✐❜✉✐çõ❡s ❧✐♠✐t❡ ♦❜t✐❞❛s ♥❛s

      ❚❛❜❡❧❛s ✈❡r✐✜❝❛✲s❡ q✉❡✱ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✱ ❛s ♠❛✐♦r❡s ❞✐❢❡r❡♥ç❛s r❡s✐❞❡♠ 2 ♥❛s ❈❧❛ss❡s ✶ ❡ 2 ✱ ❡st❡ ❢❛❝t♦ ❥✉st✐✜❝❛✲s❡ ♣♦rq✉❡ ♥❛ ❞✐str✐❜✉✐çã♦ ♣♦♥❞❡r❛❞❛ ❝♦♥s✐❞❡r❛♠✲ 1 s❡ ♦s ♣r✐♠❡✐r♦s ❛♥♦s✱ ❡ ♥❡ss❡s ❛♥♦s ❤❛✈❡rá ❛♣ó❧✐❝❡s ♥❛ ❈❧❛ss❡ 2 ✳ ◆♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱

      ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ♣♦♥❞❡r❛❞❛ ♥ã♦ ❞✐❢❡r❡ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ♦❜t✐❞❛ ♥❛ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ❡♠❜♦r❛ s❡ ✈❡r✐✜q✉❡✱ ♥❛ ❞✐str✐❜✉✐çã♦ ♣♦♥❞❡r❛❞❛✱ ✉♠❛ ♠❡♥♦r ❝♦♥❝❡♥tr❛çã♦ ❞❡ s❡❣✉r❛❞♦s ♥❛ ❝❧❛ss❡ ❞❡ ♠❛✐♦r ❞❡s❝♦♥t♦✳

      ❆s ❡s❝❛❧❛s ❞❡ ♣ré♠✐♦s✱ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ❡ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ ♣♦❞❡♠ s❡r ❝♦♥s✉❧t❛❞❛s ♥❛ ❚❛❜❡❧❛ ❚❛❜❡❧❛ ✸✳✶✹✿ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s ✭▼♦❞❡❧♦ ❞❡ ❙✐st❡♠❛ ❆❝t✉❛❧ b B (j)

      ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ▼♦❞❡❧♦ ❆❜❡rt♦ ✶ ✵✱✵✽✽✼✺✼✼✽✸ ✵✱✶✵✻✸✾✺✷✺✼ ✷ ✵✱✶✶✵✼✾✻✵✻✶ ✵✱✶✹✼✶✻✹✵✾✷ ✸ ✵✱✸✸✷✹✸✸✺✷✸ ✵✱✷✽✺✶✺✼✸✷✽ ✹ ✵✱✺✹✸✹✾✸✷✹✸ ✵✱✹✹✸✻✹✷✽✻✶ ✺ ✵✱✻✾✷✼✼✼✻✽✷ ✵✱✻✵✷✾✵✹✺✶✺ ✻ ✵✱✽✵✶✻✻✽✶✹✾ ✵✱✹✹✷✺✸✹✶✾✷

      ❆♥❛❧✐s❛♥❞♦ ❛ ❚❛❜❡❧❛ ✈❡r✐✜❝❛✲s❡ q✉❡✱ ❛ ❡s❝❛❧❛ ❞❡ ♣ré♠✐♦s ♦❜t✐❞❛ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ é ✐♥❢❡r✐♦r à ❞♦ ♠♦❞❡❧♦ ❛❜❡rt♦ ♥❛s ❝❧❛ss❡s ♥ã♦ ❛❣r❛✈❛❞❛s ✭❈❧❛ss❡ ✶ ❡ ✷✮✱ s❡♥❞♦ q✉❡ ♥❛s r❡st❛♥t❡s ❝❧❛ss❡s ❛ ❡s❝❛❧❛ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦ é ♠❡♥♦r ❞♦ q✉❡ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✳ ❆ ❡s❝❛❧❛ ♦❜t✐❞❛ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦ ♥ã♦ ❝r❡s❝❡ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ♣r♦♣❡♥sã♦ à s✐♥✐str❛❧✐❞❛❞❡✱ ❤á ✉♠❛ ❡♥♦r♠❡ q✉❡❜r❛ ♥❛ ❈❧❛ss❡ ✻✱ t❛❧ ❝♦♠♦ ❝♦♠ ♦ ♠♦❞❡❧♦ ❞❡ ❖ ♣ré♠✐♦ ♠é❞✐♦ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❢❡❝❤❛❞♦ ❡ ❛❜❡rt♦ é✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ✵✱✶✹✻✵✺✺✷ ❡ ✵✱✶✹✹✺✼✾✶✳ ❚❛❜❡❧❛ ✸✳✶✺✿ P M✱ EQM ❡ ▼❡❞✐❞❛ ❞❡ ❊✜❝✐ê♥❝✐❛ ✭▼♦❞❡❧♦ ❞❡ ❙✐st❡♠❛ ❆❝t✉❛❧

      ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ▼♦❞❡❧♦ ❆❜❡rt♦ P M

      ✵✱✶✹✺✵✺✸✻✺✶ ✵✱✶✹✺✵✺✸✻✺✶ EQM

      ✵✱✵✷✾✻✹✷✽ ✵✱✵✻✸✸✽✸✹ e(∆) ✵✱✵✸✹✶✵✺✷ ✵✱✵✷✷✾✾✸✺

      ◆❛ ❚❛❜❡❧❛ ♣♦❞❡♠ s❡r ♦❜s❡r✈❛❞♦s ♦ ♣ré♠✐♦ ♠é❞✐♦ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ♥ã♦ ❡st❛✲

      ✸✳✷ ❙✐st❡♠❛ ❇♦♥✉s ▼❛❧✉s ❆❝t✉❛❧ ❞❛ ●❛r❛♥t✐❛ ✹✺ ❚♦❞❛s ❡st❛s ♠❡❞✐❞❛s ❢♦r❛♠ ❝❛❧❝✉❧❛❞❛s ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ♥ã♦ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ♦✉ s❡❥❛✱ r❡❝♦rr❡♥❞♦ à ❞✐str✐❜✉✐çã♦ ♣♦♥❞❡r❛❞❛✳ ❱❡r✐✜❝❛✲s❡ q✉❡ ♦ ♣ré♠✐♦ ♠é❞✐♦✱ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ♥ã♦ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ❡♥tr❡ ♦s ❞♦✐s ♠♦❞❡❧♦s é ♠✉✐t♦ s❡♠❡❧❤❛♥t❡✳ ❋✐❣✉r❛ ✸✳✺✿ ❊✈♦❧✉çã♦ ❞♦ Pré♠✐♦ ▼é❞✐♦ ✭❊s❝❛❧❛ ❞❡ ❙✐st❡♠❛ ❆❝t✉❛❧

      ❆ ❋✐❣✉r❛ ✐❧✉str❛ ❛ ❡✈♦❧✉çã♦ ❞♦ ♣ré♠✐♦ ♠é❞✐♦ ❞❡ ✉♠ ♥♦✈♦ s❡❣✉r❛❞♦ ♣❛r❛ ♦s ❞♦✐s ♠♦❞❡❧♦s✱ ❛♦ ❧♦♥❣♦ ❞❡ ✷✵ ❛♥♦s✳ ❆♥❛❧✐s❛♥❞♦ ❛ ✜❣✉r❛ ✈❡r✐✜❝❛✲s❡ q✉❡✱ ♥♦ ♣r✐♠❡✐r♦ ❛♥♦✱ ♦ ♣ré♠✐♦ ♠é❞✐♦ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ é s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ✐♥❢❡r✐♦r ❛♦ ❞♦s ❛♥♦s s❡❣✉✐♥t❡s ❡ ❛♦s ❞♦ ♠♦❞❡❧♦ ❛❜❡rt♦ ❡♥q✉❛♥t♦ q✉❡✱ ♥♦s ❛♥♦s s❡❣✉✐♥t❡s✱ ♦ ♣ré♠✐♦ ♠é❞✐♦ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦ é ✐♥❢❡r✐♦r ❛♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✳ ■st♦ ❞❡✈❡✲s❡✱ ♥♦✈❛♠❡♥t❡✱ ❛♦ ❢❛❝t♦ ❞❡✱ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✱ s❡ ❡st✐♠❛r ❡①✐st✐r❡♠ ❛♣ó❧✐❝❡s ♥❛s ❝❧❛ss❡s ❞❡ ♠❛✐♦r ❛❣r❛✈❛♠❡♥t♦✱ q✉❡ t❡r✐❛♠ ❛ ♣❛❣❛r ♣ré♠✐♦s ❡❧❡✈❛❞♦s ❞❡✈✐❞♦ à ❡❧❡✈❛❞❛ s✐♥✐str❛❧✐❞❛❞❡✱ ♦ q✉❡ ♥ã♦ ❝♦rr❡s♣♦♥❞❡ à r❡❛❧✐❞❛❞❡ ♣♦✐s ❡ss❡s s❡❣✉r❛❞♦s t❡♥❞❡♠ ❛ ❛♥✉❧❛r ❛ ❛♣ó❧✐❝❡ ❝♦♠ ❡❧❡✈❛❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s✱ ❝♦♥❢♦r♠❡ ✈✐st♦ ♥❛ ❚❛❜❡❧❛ ❚❛❧ ❝♦♠♦ ♥❛s ♦✉tr❛s ❡s❝❛❧❛s✱ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ♦ ♣ré♠✐♦

      ♦

      ❡st❛❜✐❧✐③❛ ♥♦ ✷ ❛♥♦ ❡♥q✉❛♥t♦ q✉❡✱ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ ♦ ♣ré♠✐♦ ❡st❛❜✐❧✐③❛ ♣❛ss❛❞♦s ✶✺ ❛♥♦s✳

      ❆ ❋✐❣✉r❛ ✐❧✉str❛ ♦ ♣ré♠✐♦ ♠é❞✐♦✱ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ♥ã♦ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ❡♠ ❢✉♥çã♦ ❞❡ λ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❢❡❝❤❛❞♦ ❡ ♦ ❛❜❡rt♦✳ ❋✐❣✉r❛ ✸✳✻✿ ❊✈♦❧✉çã♦ ❞♦ Pré♠✐♦ ▼é❞✐♦ ❡♠ ❢✉♥çã♦ ❞❡ λ ✭❊s❝❛❧❛ ❞❡ ❙✐st❡♠❛ ❆❝t✉❛❧

      ✹✻ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✱ é ♠❡♥♦s ❛❝❡♥t✉❛❞♦ ❞♦ q✉❡ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✱ ♦ q✉❡ é ✉♠❛ ❝♦♥s❡q✉ê♥❝✐❛ ❞❛s ❡❧❡✈❛❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ s❛í❞❛ ♥❛s ❝❧❛ss❡s ♠❛✐s ❛❣r❛✈❛❞❛s✳ ❖ ▼♦❞❡❧♦ ❞❡ ●✐❧❞❡ ✫ ❙✉♥❞t ❈♦♠ ❜❛s❡ ♥❛ ❡s❝❛❧❛ ❞❡ ❛ ❡s❝❛❧❛ ❧✐♥❡❛r✱ ♦❜t✐❞❛ ♣❡❧♦ ♠♦❞❡❧♦ ❞❡ ❚❛❜❡❧❛ ✸✳✶✻✿ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s ✭▼♦❞❡❧♦ ❞❡ ❙✐st❡♠❛ ❆❝t✉❛❧ L b (j)

      ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ▼♦❞❡❧♦ ❆❜❡rt♦ ✶ ✵✱✵✻✾✵✷✹✶✷✽ ✵✱✵✽✼✶✺✸✵✶✶ ✷ ✵✱✶✽✾✷✵✽✹✹✼ ✵✱✶✺✽✹✼✾✶✽✷ ✸ ✵✱✸✵✾✸✾✷✼✻✺ ✵✱✷✷✾✽✵✺✸✺✷ ✹ ✵✱✹✷✾✺✼✼✵✽✹ ✵✱✸✵✶✶✸✶✺✷✸ ✺ ✵✱✺✹✾✼✻✶✹✵✷ ✵✱✸✼✷✹✺✼✻✾✸ ✻ ✵✱✻✻✾✾✹✺✼✷✶ ✵✱✹✹✸✼✽✸✽✻✹

      ❆♥❛❧✐s❛♥❞♦ ❛ ❡s❝❛❧❛ ❞❡ ♣ré♠✐♦s ♦❜t✐❞❛ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦s ♣ré♠✐♦s✱ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ sã♦ ✐♥❢❡r✐♦r❡s ❛♦s ❞♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✱ à ❡①❝❡♣çã♦ ❞❛ ❈❧❛ss❡ ✶✳ P♦❞❡ ❛✐♥❞❛ ♥♦t❛r✲s❡ q✉❡ ❛ ✐♥tr♦❞✉çã♦ ❞❛s r❡str✐çõ❡s ♣r♦♣♦st❛s ♣♦r ❝♦rr✐❣❡ ❛ ❞✐♠✐♥✉✐çã♦ ❞❡ ♣ré♠✐♦ q✉❡ ♦❝♦rr✐❛ ❞❛ ❈❧❛ss❡ ✺ ♣❛r❛ ❛ ❈❧❛ss❡ ✻✱ ♥❛ ❡s❝❛❧❛ ó♣t✐♠❛ ♣r♦♣♦st❛ ♣♦r

      ◆❛ ❚❛❜❡❧❛ ❛♣r❡s❡♥t❛✲s❡ ♦ ♣ré♠✐♦ ♠é❞✐♦ ❡ ♦ ❡rr♦ q✉❛❞rát✐❝♦ ♠é❞✐♦✱ ❝❛❧❝✉❧❛❞♦s ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ♥ã♦ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ t❛❧ ❝♦♠♦ ♥❛ ❡s❝❛❧❛ ❞❡ ❆ ♠❡❞✐❞❛ ❞❡ ❡✜❝✐ê♥❝✐❛ é ❞❛❞❛ ♣❡❧♦ rá❝✐♦ ❡♥tr❡ ♦s ❡rr♦s q✉❛❞rát✐❝♦ ♠é❞✐♦s ❞♦ ♠♦❞❡❧♦ ❞❡ ◆♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ♦ rá❝✐♦ é s✉♣❡r✐♦r ❛ ✶✱ ♦ q✉❡ ✐♥❞✐❝❛ q✉❡ ❤á ✉♠❛ ♣❡r❞❛ ❞❡ ❡✜❝✐ê♥❝✐❛ ♣♦r s❡ ❛❞♦♣t❛r ❛ ❡s❝❛❧❛ ❧✐♥❡❛r✱ ❡♥q✉❛♥t♦ q✉❡✱ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦ ❤á ✉♠ ❣❛♥❤♦ ❞❡ ❡✜❝✐ê♥❝✐❛✱ ✈✐st♦ q✉❡ ♦ rá❝✐♦ é ✐♥❢❡r✐♦r ❛ ✶✳ ❚❛❜❡❧❛ ✸✳✶✼✿ P M✱ EQM ❡ ▼❡❞✐❞❛ ❞❡ ❊✜❝✐ê♥❝✐❛ ✭▼♦❞❡❧♦ ❞❡ ❙✐st❡♠❛ ❆❝t✉❛❧

      ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ▼♦❞❡❧♦ ❆❜❡rt♦ P M

      ✵✱✶✹✶✼✻✽✵✻✸ ✵✱✶✹✶✼✶✻✺✺✻ EQM EQM (L) ✵✱✵✸✶✽✸✹✼ ✵✱✵✹✶✷✹✵✼ EQM (B) ✶✱✵✼✸✾✹ ✵✱✻✺✵✻✺✹✺✽✽

      ✸✳✷ ❙✐st❡♠❛ ❇♦♥✉s ▼❛❧✉s ❆❝t✉❛❧ ❞❛ ●❛r❛♥t✐❛ ✹✼ ❋✐❣✉r❛ ✸✳✼✿ ❊✈♦❧✉çã♦ ❞♦ Pré♠✐♦ ▼é❞✐♦ ✭❊s❝❛❧❛ ❞❡ ❙✐st❡♠❛ ❆❝t✉❛❧ ❖ ▼♦❞❡❧♦ ❞❡ ❆♥❞r❛❞❡ ❡ ❙✐❧✈❛ ❈♦♠ ❜❛s❡ ♥❛ ❡s❝❛❧❛ ❞❡ ❛ ❡s❝❛❧❛ ❣❡✲ ♦♠étr✐❝❛✱ ♦❜t✐❞❛ ♣❡❧♦ ♠♦❞❡❧♦ ❞❡ ♣♦❞❡ s❡r ❝♦♥s✉❧t❛❞❛ ♥❛ ❚❛❜❡❧❛ ❚❛❜❡❧❛ ✸✳✶✽✿ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s ✭▼♦❞❡❧♦ ❞❡ ❙✐st❡♠❛ ❆❝t✉❛❧ G b (j)

      ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ▼♦❞❡❧♦ ❆❜❡rt♦ ✶ ✵✱✵✾✷✼✾✵✹ ✵✱✵✾✼✽✸✸✾✽✽ ✷ ✵✱✶✺✾✹✼✸✵✼✺ ✵✱✶✺✸✷✷✵✸✷✺ ✸ ✵✱✷✼✹✵✼✻✹✸✶ ✵✱✷✸✾✾✻✷✷✾✸ ✹ ✵✱✹✼✶✵✸✽✵✼✷ ✵✱✸✼✺✽✶✶✶✷ ✺ ✵✱✽✵✾✺✹✸✼✻✸ ✵✱✺✽✽✺✻✼✹✻✸ ✻ ✶✱✸✾✶✸✶✷✸✽✽ ✵✱✾✷✶✼✼✵✻✹✹

      ❆♥❛❧✐s❛♥❞♦ ❛ ❡s❝❛❧❛ ♦❜t✐❞❛✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦s ♣ré♠✐♦s ❞♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ sã♦ s✉♣❡✲ r✐♦r❡s ❛♦s ❞♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ ❡①❝❡♣t♦ ♥❛ ❈❧❛ss❡ ✶✳ ❚❛❜❡❧❛ ✸✳✶✾✿ P M✱ EQM ❡ ▼❡❞✐❞❛ ❞❡ ❊✜❝✐ê♥❝✐❛ ✭▼♦❞❡❧♦ ❞❡ ❙✐st❡♠❛ ❆❝t✉❛❧

      ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ▼♦❞❡❧♦ ❆❜❡rt♦ P M

      ✵✱✶✹✾✹✼✻✶✸✹ ✵✱✶✹✺✶✾✷✽✶ EQM EQM (G) ✵✱✵✸✶✷✸✹✹ ✵✱✵✹✵✾✽✷✹ EQM (B) ✶✱✵✺✸✻✾ ✵✱✻✹✻✺✼✾✸✽✽

      ✹✽ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❝♦♥❞✐çõ❡s ❞❡ ♥ã♦ ❡st❛❝✐♦♥❛r✐❞❛❞❡✳ ❆♥❛❧✐s❛♥❞♦ ❡st❛ t❛❜❡❧❛✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦ ♣ré♠✐♦ ♠é❞✐♦ ❡st✐♠❛❞♦ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ é s✉♣❡r✐♦r ❛♦ ❡st✐♠❛❞♦ ♣❡❧♦ ♠♦❞❡❧♦ ❛❜❡rt♦✳ ❖ rá❝✐♦ ❡♥tr❡ ♦ ❡rr♦ q✉❛❞rát✐❝♦ ♠é❞✐♦ ❞❛ ❡s❝❛❧❛ ❞❡ ❡ ❛ ❡s❝❛❧❛ ❣❡♦♠étr✐❝❛ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ é s✉♣❡r✐♦r ❛ ✶✱ ♣♦rt❛♥t♦✱ ❤á ✉♠❛ ♣❡r❞❛ ❞❡ ❡✜❝✐ê♥❝✐❛ ❛♦ ❝♦♥s✐❞❡r❛r ❛ ❡s❝❛❧❛ ❣❡♦♠étr✐❝❛✱ ❡♥q✉❛♥t♦ q✉❡ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦ ❤á ✉♠ ❣❛♥❤♦ ❞❡ ❡✜❝✐ê♥❝✐❛ ❛♦ ❛❞♦♣t❛r ❡st❛ ❡s❝❛❧❛✳

      ❆ ❋✐❣✉r❛ ✐❧✉str❛ ❛ ❡✈♦❧✉çã♦ ❞♦ ♣ré♠✐♦ ❞❡ ✉♠ ♥♦✈♦ s❡❣✉r❛❞♦ ❛♦ ❧♦♥❣♦ ❞❡ ✷✵ ❛♥♦s✳ ❋✐❣✉r❛ ✸✳✽✿ ❊✈♦❧✉çã♦ ❞♦ Pré♠✐♦ ▼é❞✐♦ ✭❊s❝❛❧❛ ❞❡ ❙✐st❡♠❛ ❆❝t✉❛❧

      ❆ ❋✐❣✉r❛ ✐❧✉str❛ ♦ ♣ré♠✐♦ ♠é❞✐♦✱ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ♥ã♦ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ❡♠ ❢✉♥çã♦ ❞❡ λ✱ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❢❡❝❤❛❞♦ ❡ ❛❜❡rt♦✳ ❋✐❣✉r❛ ✸✳✾✿ ❊✈♦❧✉çã♦ ❞♦ ♣ré♠✐♦ ♠é❞✐♦ ❡♠ ❢✉♥çã♦ ❞❡ λ ✭❊s❝❛❧❛ ❞❡ ❙✐st❡♠❛ ❆❝t✉❛❧

      ✸✳✷✳✺ ▼❡❞✐❞❛s ❞❡ ❆✈❛❧✐❛çã♦

      ◆❡st❛ s❡❝çã♦ s❡rã♦ ❞❡t❡r♠✐♥❛❞❛s ❛s ♠❡❞✐❞❛s ❞❡ ❛✈❛❧✐❛çã♦ ❡♥✉♥❝✐❛❞❛s ♥♦ ❈❛♣ít✉❧♦ ✉t✐❧✐③❛♥❞♦ ❛s ❡s❝❛❧❛s ó♣t✐♠❛s ❞❡ ♣ré♠✐♦s✱ ❛ ❡s❝❛❧❛ ❛❝t✉❛❧ ❡ ❛s ❞✐str✐❜✉✐çõ❡s ❧✐♠✐t❡ ❡

      ✸✳✷ ❙✐st❡♠❛ ❇♦♥✉s ▼❛❧✉s ❆❝t✉❛❧ ❞❛ ●❛r❛♥t✐❛ ✹✾ ◆í✈❡❧ ▼é❞✐♦ ❘❡❧❛t✐✈♦ ❞❡ ❊st❛❝✐♦♥❛r✐❞❛❞❡ ◆❛ ❚❛❜❡❧❛ ♣♦❞❡ s❡r ♦❜s❡r✈❛❞♦ ♦ ◆í✈❡❧ ▼é❞✐♦ ❘❡❧❛t✐✈♦ ❞❡ ❊st❛❝✐♦♥❛r✐❞❛❞❡ ♦❜t✐❞♦ ♣❛r❛ ✉♠ s❡❣✉r❛❞♦ r❡t✐r❛❞♦ ❛♦ ❛❝❛s♦ ❞❛ ❝❛rt❡✐r❛ ❞❡ ❛♣ó❧✐❝❡s✳

      ❚❛❜❡❧❛ ✸✳✷✵✿ ◆í✈❡❧ ▼é❞✐♦ ❘❡❧❛t✐✈♦ ❞❡ ❊st❛❝✐♦♥❛r✐❞❛❞❡✿ ❙✐st❡♠❛ ❆❝t✉❛❧ RSAL

      ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ▼♦❞❡❧♦ ❆❜❡rt♦ ❊s❝❛❧❛ ❆❝t✉❛❧ ✵✱✵✼✹✾✵✷✹ ✵✱✶✻✾✸✽✾✺✹✾

      ◆♦r❜❡r❣ ✵✱✵✼✾✸✶✷✾ ✵✱✵✽✻✻✽✸✽ ❇♦r❣❛♥ ❡t ❛❧ ✵✱✵✼✽✾✻✻✸ ✵✱✵✼✼✽✻✵✹

      ●✐❧❞❡ ✫ ❙✉♥❞t ✵✱✶✷✻✺✷✷ ✵✱✶✻✷✸✺✺ ❆✳ ❙✐❧✈❛ ✵✱✵✹✸✻✺✹ ✵✱✵✺✼✹✼✽✼

      ❆♥❛❧✐s❛♥❞♦ ❛ ❚❛❜❡❧❛ ✈❡r✐✜❝❛✲s❡ q✉❡✱ ❡♠ q✉❛❧q✉❡r ✉♠ ❞♦s ♠♦❞❡❧♦s ❡ ♣❛r❛ q✉❛❧q✉❡r ✉♠❛ ❞❛s ❡s❝❛❧❛s✱ ♦ RSAL é ♠✉✐t♦ ❜❛✐①♦✱ ♦ q✉❡ ✐♥❞✐❝❛ ❡①✐st✐r ✉♠❛ ❣r❛♥❞❡ ❛❣❧♦♠❡r❛çã♦ ❞❡ s❡❣✉r❛❞♦s ♥❛s ❝❧❛ss❡s ♠❛✐s ❜❛✐①❛s ❞♦ s✐st❡♠❛✳ ❊st❡ ❢❛❝t♦ ❞❡✈❡✲s❡✱ ❡ss❡♥❝✐❛❧♠❡♥t❡✱ à ♣♦✉❝❛ s❡✈❡r✐❞❛❞❡ ❞❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦ ❜❡♠ ❝♦♠♦ à s✉❛ ✐♥❝♦❡rê♥❝✐❛✳ ❱❡r✐✜❝❛✲s❡ ❛✐♥❞❛ q✉❡ ♦ RSAL✱ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ é s✉♣❡r✐♦r ❛♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✱ à ❡①❝❡♣çã♦ ❞❛ ❡s❝❛❧❛ ❞❡ ♦♥❞❡ ❛ ❞✐❢❡r❡♥ç❛ é ♣♦✉❝♦ s✐❣♥✐✜❝❛t✐✈❛✳

      ❆ ❋✐❣✉r❛ ✐❧✉str❛ ❛ ❡✈♦❧✉çã♦ ❞❡ RSAL✱ ❡♠ ❢✉♥çã♦ ❞❡ λ✱ ♣❛r❛ ♦s ❞♦✐s ♠♦❞❡❧♦s✳ ❋✐❣✉r❛ ✸✳✶✵✿ RSAL ❡♠ ❢✉♥çã♦ ❞❡ λ✿ ❙✐st❡♠❛ ❆❝t✉❛❧

      ❈♦❡✜❝✐❡♥t❡ ❞❡ ❱❛r✐❛çã♦ ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ♦ ❈♦❡✜❝✐❡♥t❡ ❞❡ ❱❛r✐❛çã♦ ❞❡ Pré♠✐♦s✱ ♣❛r❛ t♦❞❛s ❛s ❡s❝❛❧❛s✱ ♣❛r❛ ✉♠ s❡❣✉r❛❞♦ r❡t✐r❛❞♦ ❛♦ ❛❝❛s♦ ❞❛ ❝❛rt❡✐r❛ ❞❡ ❛♣ó❧✐❝❡s✳

      ❆♥❛❧✐s❛♥❞♦ ❛ ❚❛❜❡❧❛ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ✈❛r✐❛çã♦ ❞♦ ♣ré♠✐♦ ♠é❞✐♦✱ ❡♠ q✉❛❧q✉❡r ✉♠ ❞♦s ♠♦❞❡❧♦s✱ ♣❛r❛ q✉❛❧q✉❡r ✉♠❛ ❞❛s ❡s❝❛❧❛s✱ é ♠✉✐t♦ ❜❛✐①❛✳ ◆♦ ❡♥t❛♥t♦✱ ✈❡r✐✜❝❛✲s❡ q✉❡✱ ❡①✐st❡ ♠❛✐♦r ✈❛r✐❛❜✐❧✐❞❛❞❡ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✱ ♦ q✉❡ ♣♦❞❡ s❡r ❥✉st✐✜❝❛❞♦✱ ♣❡❧♦ ❢❛❝t♦

      ✺✵ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❚❛❜❡❧❛ ✸✳✷✶✿ ❈♦❡✜❝✐❡♥t❡ ❞❡ ❱❛r✐❛çã♦ ❞❡ Pré♠✐♦s✿ ❙✐st❡♠❛ ❆❝t✉❛❧

      CV ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ▼♦❞❡❧♦ ❆❜❡rt♦

      ❊s❝❛❧❛ ❆❝t✉❛❧ ✵✱✷✹✼✽✶✷ ✵✱✶✻✺✷✹✻ ◆♦r❜❡r❣ ✵✱✽✷✹✵✹✾ ✵✱✸✻✵✶✽✶

      ❇♦r❣❛♥ ❡t ❛❧ ✵✱✼✽✼✾✽✼ ✵✱✸✵✹✻✻✵ ●✐❧❞❡ ✫ ❙✉♥❞t ✵✱✼✶✽✽✺✷ ✵✱✷✻✹✵✷✸

      ❆♥❞r❛❞❡ ❡ ❙✐❧✈❛ ✵✱✻✼✹✻✽✶ ✵✱✷✽✷✻✽✸ ❆ ❋✐❣✉r❛ ✐❧✉str❛ ❛ ❡✈♦❧✉çã♦ ❞♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✈❛r✐❛çã♦ ❞♦ ♣ré♠✐♦ ❡♠ ❢✉♥çã♦ ❞❛

      ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✳ ❋✐❣✉r❛ ✸✳✶✶✿ CV ❡♠ ❢✉♥çã♦ ❞❡ λ✿ ❙✐st❡♠❛ ❆❝t✉❛❧

      ❆ ❊❧❛st✐❝✐❞❛❞❡ ❞♦ Pré♠✐♦ ❆ ❡❧❛st✐❝✐❞❛❞❡ ❣❧♦❜❛❧ ❞♦ ♣ré♠✐♦ ♠é❞✐♦✱ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ❝♦♠♦ ❥á ❢♦✐ r❡❢❡r✐❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ♠❡❞❡ ❛ r❡s♣♦st❛ ❞♦ s✐st❡♠❛ ❛ ✉♠❛ ❛❧t❡r❛çã♦ ♥❛ ❢r❡q✉ê♥❝✐❛ ❡s♣❡r❛❞❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✳

      ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ❛ ❊❧❛st✐❝✐❞❛❞❡ ●❧♦❜❛❧ ❞♦ s✐st❡♠❛ ♣❛r❛ ✉♠ s❡❣✉r❛❞♦ r❡t✐r❛❞♦ ❛♦ ❛❝❛s♦ ❞❛ ❝❛rt❡✐r❛ ❞❡ ❛♣ó❧✐❝❡s✳

      ❚❛❜❡❧❛ ✸✳✷✷✿ ❆ ❊❧❛st✐❝✐❞❛❞❡ ●❧♦❜❛❧ ❞♦ ❙✐st❡♠❛✿ ❙✐st❡♠❛ ❆❝t✉❛❧ η

      ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ▼♦❞❡❧♦ ❆❜❡rt♦ ❊s❝❛❧❛ ❆❝t✉❛❧ ✵✱✵✽✹✶✺✹✸ ✵✱✵✹✸✹✻✾✹

      ◆♦r❜❡r❣ ✵✱✷✹✼✷✻✽ ✵✱✶✵✻✸✼✷ ❇♦r❣❛♥ ❡t ❛❧ ✵✱✷✹✾✸✺✽ ✵✱✵✾✵✽✻✺✷

      ●✐❧❞❡ ✫ ❙✉♥❞t ✵✱✷✻✽✸✹✻ ✵✱✵✽✶✾✶✵✺ ❆✳ ❙✐❧✈❛ ✵✱✷✷✺✵✵✺ ✵✱✶✺✵✷✹✹

      ❊♠ q✉❛❧q✉❡r ✉♠ ❞♦s ♠♦❞❡❧♦s✱ ♣❛r❛ q✉❛❧q✉❡r ✉♠❛ ❞❛s ❡s❝❛❧❛s✱ ✈❡r✐✜❝❛✲s❡ q✉❡✱ ❛

      ✸✳✷ ❙✐st❡♠❛ ❇♦♥✉s ▼❛❧✉s ❆❝t✉❛❧ ❞❛ ●❛r❛♥t✐❛ ✺✶ ❛✈❛❧✐❛❞❛ s❡❣✉♥❞♦ ♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ é s✉♣❡r✐♦r ❛ ❞♦ ♠♦❞❡❧♦ ❛❜❡rt♦✳ ■st♦ ❥✉st✐✜❝❛✲s❡ ♣❡❧♦ ❢❛❝t♦ ❞♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ♥ã♦ ❝♦♥s✐❞❡r❛r ❛s s❛í❞❛s ❞❡ ❛♣ó❧✐❝❡s ♥♦ s✐st❡♠❛✳

      ❋✐❣✉r❛ ✸✳✶✷✿ ❊❧❛st✐❝✐❞❛❞❡ ●❧♦❜❛❧ ❡♠ ❢✉♥çã♦ ❞❡ λ✿ ❙✳ ❆❝t✉❛❧ ❆ ❊❧❛st✐❝✐❞❛❞❡ ❚r❛♥s✐❡♥t❡ ❈♦♠♦ ❥á ❢♦✐ r❡❢❡r✐❞♦ ♥❛ ❙✉❜✲s❡❝çã♦ ❛ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡ ♠❡❞❡ ❛ ❡❧❛st✐❝✐❞❛❞❡ ❞♦ ✈❛❧♦r ❡s♣❡r❛❞♦ ❛❝t✉❛❧✐③❛❞♦ ❞♦s ♣❛❣❛♠❡♥t♦s ❢✉t✉r♦s✱ ❡♠ r❡❧❛çã♦ à ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✳ ❉❛❞♦ q✉❡ ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ ♥❛s ❝❧❛ss❡s ❝♦♠ í♥❞✐❝❡ ✶ ❡ ✷ sã♦ ❞✐st✐♥t❛s✱ ♦♣t♦✉✲s❡ ♣♦r ❛♥❛❧✐s❛r ❛ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡ ♣❛r❛ ❛s ✶✶ ❝❧❛ss❡s ❞♦ s✐st❡♠❛✳

      ❈♦♥s✐❞❡r❛♥❞♦ ✉♠❛ t❛①❛ ❞❡ ❞❡s❝♦♥t♦ β = 0, 97✱ ❛ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡ ♣❛r❛ ♦s ♠♦✲ ❞❡❧♦s ❢❡❝❤❛❞♦ ❡ ❛❜❡rt♦ ♣♦❞❡♠ s❡r ❝♦♥s✉❧t❛❞❛s ♥❛s ❚❛❜❡❧❛s r❡s♣❡❝t✐✈❛♠❡♥t❡✳

      ❚❛❜❡❧❛ ✸✳✷✸✿ ❆ ❊❧❛st✐❝✐❞❛❞❡ ❚r❛♥s✐❡♥t❡ ✭▼♦❞❡❧♦ ❋❡❝❤❛❞♦✮✿ ❙✐st❡♠❛ ❆❝t✉❛❧ ❥ ❊✳ ❆❝t✉❛❧ ◆♦r❜❡r❣ ❇♦r❣❛♥ ❡t ❛❧ ●✐❧❞❡ ❡ ❙✉♥❞t ❆✳ ❙✐❧✈❛

      ✶ ✵✱✵✽✶✹✾✻✷ ✵✱✷✹✶✽✺✹ ✵✱✷✹✸✾✷✸ ✵✱✷✻✷✼✸✹ ✵✱✷✶✾✽✺✽

      2 2 ✵✱✵✽✵✻✺✽✻ ✵✱✷✸✾✷✵✾ ✵✱✷✹✷✾✷ ✵✱✷✺✺✻✺✹ ✵✱✷✶✼✶✸✸

      2 1 ✵✱✵✼✾✵✾✺✶ ✵✱✷✸✻✷✵✹ ✵✱✷✹✶✼✻✾ ✵✱✷✹✽✵✸✸ ✵✱✷✶✸✾✺✶

      3 2 ✵✱✵✽✵✷✹✻✸ ✵✱✷✸✶✺✵✷ ✵✱✷✸✸✸✷✹ ✵✱✷✹✽✾✾✽ ✵✱✷✶✷✻✷✷

      3 1 ✵✱✵✼✼✾✷✼✸ ✵✱✷✷✵✸✽✼ ✵✱✷✷✶✾✾ ✵✱✷✸✹✽✼✸ ✵✱✷✵✹✹✻✺

      4 2 ✵✱✵✼✾✽✸✽✸ ✵✱✷✷✸✶✻✼ ✵✱✷✷✹✾✹✺ ✵✱✷✹✷✼✷✺ ✵✱✷✵✺✸✸✼

      4 1 ✵✱✵✼✻✼✽✵✹ ✵✱✷✵✹✷✺✻ ✵✱✷✵✺✽✶✺ ✵✱✷✷✷✾✾✼ ✵✱✶✽✾✽✺

      5 2 ✵✱✵✼✾✹✸✹✺ ✵✱✷✶✼✻✶✹ ✵✱✷✶✾✹✶✸ ✵✱✷✸✻✼✾✾ ✵✱✶✾✹✵✷✷

      5 1 ✵✱✵✼✺✻✺✹ ✵✱✶✾✹✵✵✼ ✵✱✶✾✺✻✷✽ ✵✱✷✶✷✷✵✼ ✵✱✶✻✽✻✻✾

      6 2 ✵✱✵✼✼✾✽✽✽ ✵✱✷✶✸✼✷✽ ✵✱✷✶✺✺✻✹ ✵✱✷✸✶✶✾ ✵✱✶✼✼✹✺

      6 1 ✵✱✵✼✶✻✽✾✸ ✵✱✶✽✼✵✺✹ ✵✱✶✽✽✼✺✸ ✵✱✷✵✷✸✹✹ ✵✱✶✹✵✹✸

      ❆♥❛❧✐s❛♥❞♦ ❛ ❡❧❛st✐❝✐❞❛❞❡ ❞♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ❡s❝❛❧❛ ❛❝t✉❛❧ ❛✲ ♣r❡s❡♥t❛ ✈❛❧♦r❡s ♣❛r❛ ❛ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡ ✐♥❢❡r✐♦r❡s ❡♠ t♦❞❛s ❛s ❝❧❛ss❡s q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦ ❝♦♠ ❛s ♦✉tr❛s ❡s❝❛❧❛s✱ ❡♥q✉❛♥t♦ q✉❡ ❛ ❡s❝❛❧❛ ❧✐♥❡❛r ❞❡

      ✺✷ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❚❛❜❡❧❛ ✸✳✷✹✿ ❆ ❊❧❛st✐❝✐❞❛❞❡ ❚r❛♥s✐❡♥t❡ ✭▼♦❞❡❧♦ ❆❜❡rt♦✮✿ ❙✐st❡♠❛ ❆❝t✉❛❧

      ❥ ❊✳ ❆❝t✉❛❧ ◆♦r❜❡r❣ ❇♦r❣❛♥ ❡t ❛❧ ●✐❧❞❡ ❡ ❙✉♥❞t ❆✳ ❙✐❧✈❛ ✶ ✵✱✵✵✺✼✽✷ ✵✱✶✸✶✽✽✽ ✵✱✵✽✷✽✵✶✽ ✵✱✵✼✵✼✾✵ ✵✱✵✼✼✼✵✸

      2 2 ✵✱✵✵✹✽✻✷ ✵✱✶✶✶✵✺✶ ✵✱✵✼✷✹✸✺ ✵✱✵✺✻✷✷✾ ✵✱✵✻✺✷✾✻

      2 1 ✵✱✵✵✶✶✵✾ ✵✱✵✶✾✻✶✼ ✵✱✵✶✸✹✼✵ ✵✱✵✵✼✾✹✷ ✵✱✵✶✵✽✼✶

      3 2 ✵✱✵✵✹✻✵✾ ✵✱✵✽✶✶✶✵ ✵✱✵✺✻✺✼✾ ✵✱✵✹✽✷✷✼ ✵✱✵✺✺✵✼✷

      3 1 ✵✱✵✵✸✹✹✾ ✵✱✵✺✸✸✻✼ ✵✱✵✸✾✵✻✾ ✵✱✵✸✶✽✻✹ ✵✱✵✹✵✵✺✽

      4 2 ✵✱✵✵✹✸✹✼ ✵✱✵✻✶✶✸✷ ✵✱✵✹✹✼✽✼ ✵✱✵✹✶✽✷✵ ✵✱✵✹✸✽✶✽

      4 1 ✵✱✵✵✵✾✸✻ ✵✱✵✷✻✶✾✷ ✵✱✵✶✾✵✵✸ ✵✱✵✷✵✷✽✶ ✵✱✵✶✾✾✹✼

      5 2 ✵✱✵✵✸✾✹✶ ✵✱✵✹✽✻✽✵ ✵✱✵✸✹✽✶✶ ✵✱✵✸✹✾✸✶ ✵✱✵✸✶✷✸✶

      5 1 ✵✱✵✵✶✵✷✶✸✼ ✵✱✵✶✹✶✸✼✷ ✵✱✵✵✼✶✾✺✸✸ ✵✱✵✶✷✷✷✶ ✵✱✵✵✸✸✽✹

      6 2 ✵✱✵✵✵✼✾✻ ✵✱✵✵✽✼✸✾ ✵✱✵✵✾✽✷✼ ✵✱✵✵✻✼✻✸ ✵✱✵✵✹✷✼✶

      6 1 ✵✱✵✵✶✸✾✵ ✵✱✵✵✵✽✺✺ ✵✱✵✵✸✶✻✽ ✵✱✵✵✶✸✽✸ ✲✵✱✵✵✵✽✵✵

      ❙♦❜ ❛ ♣❡rs♣❡❝t✐✈❛ ❞♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ❡s❝❛❧❛ ❛❝t✉❛❧ ❛♣r❡s❡♥t❛ ✈❛❧♦r❡s 1 ♣❛r❛ ❛ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡ ✐♥❢❡r✐♦r❡s ❡♠ t♦❞❛s ❛s ❝❧❛ss❡s✱ à ❡①❝❡♣çã♦ ❞❛ ❝❧❛ss❡ 6 1

      ❡♥q✉❛♥t♦ q✉❡✱ ❞❛ ❈❧❛ss❡ ✶ à ❈❧❛ss❡ 5 ✱ ❛ ❡s❝❛❧❛ ❞❡ ❛♣r❡s❡♥t❛ ✈❛❧♦r❡s ♣❛r❛ ❛ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡ s✉♣❡r✐♦r às ♦✉tr❛s ❡s❝❛❧❛s✱ ❡ ♥❛ ❝❧❛ss❡ ♠❛✐s ❛❣r❛✈❛❞❛ 2 1

      ✭❈❧❛ss❡ 6 ❡ ❈❧❛ss❡ 6 ✮ ❛ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡ é ♠❛✐♦r ♣❛r❛ ❛ ❡s❝❛❧❛ ❞❡

      ❈♦♠♣❛r❛♥❞♦ ♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ❝♦♠ ♦ ❛❜❡rt♦✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥✲ s✐❡♥t❡ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ❛♣r❡s❡♥t❛ ✈❛❧♦r❡s ❜❛st❛♥t❡s s✉♣❡r✐♦r❡s✱ ❡♠ t♦❞❛s ❛s ❝❧❛ss❡s✳ ❊st❡ ❢❛❝t♦ ❞❡✈❡✲s❡✱ ♥♦✈❛♠❡♥t❡✱ às ❡❧❡✈❛❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ s❛í❞❛ ♥❛s ❝❧❛ss❡s ♠❛✐s ❛❣r❛✈❛❞❛s ♦ q✉❡ s❡ tr❛❞✉③✐rá✱ ♥❛t✉r❛❧♠❡♥t❡✱ ♥✉♠ ✈❛❧♦r ✐♥❢❡r✐♦r ♣❛r❛ ♦ ✈❛❧♦r ❡s♣❡r❛❞♦✱ ❛❝t✉❛❧✐③❛❞♦✱ ❞♦s ♣❛❣❛♠❡♥t♦s ❢✉t✉r♦s✱ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦ ❝♦♠ ♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✱ ♦♥❞❡ ❡st❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ♥ã♦ sã♦ t✐❞❛s ❡♠ ❝♦♥t❛✳

      ✸✳✷✳✻ ❈♦♠❡♥tár✐♦s às ❊s❝❛❧❛s Ó♣t✐♠❛s

      ❉❛❞♦ q✉❡ ♦s ❞♦✐s ♠♦❞❡❧♦s sã♦ ❝♦♥str✉í❞♦s s♦❜ ♣r❡ss✉♣♦st♦s ❞✐❢❡r❡♥t❡s✱ s❡rã♦ ❢❡✐t❛s ❛♥á❧✐s❡s ❝♦♠♣❛r❛t✐✈❛s ❡♥tr❡ ❛s ❡s❝❛❧❛s ♦❜t✐❞❛s ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ❡✱ ♣♦st❡r✐♦r♠❡♥t❡✱ ❡♥tr❡ ❛s ♦❜t✐❞❛s ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦✳ ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ❆s ❡s❝❛❧❛s ó♣t✐♠❛s ❞❡ ♣ré♠✐♦s ♦❜t✐❞❛ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ❞❡ ❡ ❞♦ ♠♦❞❡❧♦ ❞❡ ❛♣r❡s❡♥t❛♠ ✈❛❧♦r❡s ♠✉✐t♦ s❡♠❡❧❤❛♥t❡s✳ ❊st❡ r❡s✉❧t❛❞♦ é ❡①♣❡❝tá✈❡❧✱ ✈✐st♦ q✉❡✱ ❝♦♠♦ ❥á ❢♦✐ r❡❢❡r✐❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ♦ ♠♦❞❡❧♦ ❞❡ ❖ q✉❡ ❞✐❢❡r❡♥❝✐❛ ❡st❡s ❞♦✐s ♠♦❞❡❧♦s é ♦ ❢❛❝t♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ❡st✐♠❛r ✉♠❛

      ✸✳✷ ❙✐st❡♠❛ ❇♦♥✉s ▼❛❧✉s ❆❝t✉❛❧ ❞❛ ●❛r❛♥t✐❛ ✺✸ s✐st❡♠❛✳ ❉❛❞♦ q✉❡ ❝♦♠ ❛s ❛❝t✉❛✐s r❡❣r❛s ❞❡ tr❛♥s✐çã♦ ❞♦ SBM ❞❛ ●❛r❛♥t✐❛✱ ♦ s✐st❡♠❛ ❛t✐♥❣❡ ❛ ❡st❛❝✐♦♥❛r✐❞❛❞❡ ❧♦❣♦ ♥♦ s❡❣✉♥❞♦ ❛♥♦✱ ♣❡❧♦ q✉❡ ❛ ❡st❛❝✐♦♥❛r✐❞❛❞❡ t❡rá ✉♠ ♣❡s♦ ❡❧❡✈❛❞♦ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛ ❡s❝❛❧❛ ❞❡ ♣♦rt❛♥t♦ é ♥❛t✉r❛❧ q✉❡ ♦s ♣ré♠✐♦s s❡❥❛♠ s❡♠❡❧❤❛♥t❡s✳

      ❆ ❡s❝❛❧❛ ❧✐♥❡❛r✱ ♦❜t✐❞❛ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ❞❡ r❡✈❡❧❛✲s❡ s❡r ❛ ♠❡♥♦s s❡✈❡r❛ ♣❛r❛ ♦s s❡❣✉r❛❞♦s q✉❡ ❞❡❝❧❛r❡♠ ♠✉✐t♦s s✐♥✐str♦s✱ ✐st♦ ♣♦rq✉❡✱ ❡♠ ❝♦♠♣❛r❛çã♦ ❝♦♠ ❛s r❡st❛♥t❡s ❡s❝❛❧❛s ❡st✐♠❛❞❛s✱ ❡st❛ é ❛ q✉❡ ❛♣r❡s❡♥t❛ ♣ré♠✐♦s s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ♠❛✐s ❜❛✐①♦s ♣❛r❛ ❛s ❝❧❛ss❡s ♠❛✐s ❛❣r❛✈❛❞❛s ❞♦ s✐st❡♠❛✳

      ❆ ❡s❝❛❧❛ ❣❡♦♠étr✐❝❛✱ ♦❜t✐❞❛ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ❞❡ ✭❚❛❜❡❧❛ é ❛ ❡s❝❛❧❛ ♠❛✐s s❡✈❡r❛✱ ✐st♦ ♣♦rq✉❡ ❛♣r❡s❡♥t❛ ✉♠ ♣ré♠✐♦ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ s✉✲ ♣❡r✐♦r ♥❛s ❝❧❛ss❡s ♠❛✐s ❛❣r❛✈❛❞❛s✱ ❡♠ ❝♦♠♣❛r❛çã♦ ❝♦♠ ❛s ♦✉tr❛s ❡s❝❛❧❛s✳

      ❊♠ r❡❧❛çã♦ ❛♦ ❡rr♦ q✉❛❞rát✐❝♦ ♠é❞✐♦✱ ✈❡r✐✜❝❛✲s❡ q✉❡ q✉❡ ❛ ❡s❝❛❧❛ ❞❡ é ❛ q✉❡ ❛♣r❡s❡♥t❛ ✉♠ EQM ✐♥❢❡r✐♦r✱ ♠❛s ❡ss❛ ❞✐❢❡r❡♥ç❛ ♥ã♦ é s✐❣♥✐✜❝❛t✐✈❛ ❡♠ ❝♦♠✲ ♣❛r❛çã♦ ❝♦♠ ❛s ♦✉tr❛s ❡s❝❛❧❛s✳ ❈♦♠♣❛r❛♥❞♦ ❛ ❡✜❝✐ê♥❝✐❛ ❞❛ ❡s❝❛❧❛ ❞❡ ❝♦♠ ❛ ❡s❝❛❧❛ ❞❡ é ♠❛✐s ❡✜❝✐❡♥t❡✱ ♥♦ ❡♥t❛♥t♦ ❡ss❛ ❞✐❢❡r❡♥ç❛ ♥ã♦ é s✐❣♥✐✜❝❛t✐✈❛✳ ❚❡♥❞♦ ❡♠ ❝♦♥t❛ ❛ ♠❡❞✐❞❛ ❞❛ ♣❡r❞❛ ❞❡ ❡✜❝✐ê♥❝✐❛✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ❤á ✉♠❛ ♣❡r❞❛ ❞❡ ❡✜❝✐ê♥❝✐❛ ❛♦ ❛❞♦♣t❛r à ❡s❝❛❧❛ ❧✐♥❡❛r ♦✉ ❣❡♦♠étr✐❝❛✱ ♥♦ ❡♥t❛♥t♦ ❡ss❛ ♣❡r❞❛ ♥ã♦ é s✐❣♥✐✜❝❛t✐✈❛✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ s❡ s❡ ❝♦♥s✐❞❡r❛r ❛ ❡s❝❛❧❛ ❣❡♦♠étr✐❝❛✳

      ❊♠ r❡❧❛çã♦ às ♠❡❞✐❞❛s ❞❡ ❛✈❛❧✐❛çã♦ ♣r♦♣♦st❛s ♣♦r ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ❡s❝❛❧❛ ❧✐♥❡❛r é ❛ q✉❡ ❛♣r❡s❡♥t❛ ✈❛❧♦r❡s s✉♣❡r✐♦r❡s ❡♠ t♦❞❛s ❛s ♠❡❞✐❞❛s✱ à ❡①❝❡♣çã♦ ❞♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✈❛r✐❛çã♦ ❞♦s ♣ré♠✐♦s✳ ❘❡❧❛t✐✈❛♠❡♥t❡ ❛♦ RSAL ♦ ✈❛❧♦r ♦❜t✐❞♦ ♣❡❧❛ ❡s❝❛❧❛ ❧✐♥❡❛r✱ ❞❡✈❡✲s❡ ❡ss❡♥❝✐❛❧♠❡♥t❡ ❛♦ ❢❛❝t♦ ❞❡st❛ ❡s❝❛❧❛ ❛♣r❡s❡♥t❛r ✉♠ ♣ré♠✐♦ ♠á①✐♠♦ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ✐♥❢❡r✐♦r às r❡st❛♥t❡s ❡s❝❛❧❛s✳

      ❚❛❜❡❧❛ ✸✳✷✺✿ ❊s❝❛❧❛s Ó♣t✐♠❛s ❡♠ P❡r❝❡♥t❛❣❡♠ ✭▼♦❞❡❧♦ ❋❡❝❤❛❞♦✮✿ ❙✳ ❆❝t✉❛❧ j ◆♦r❜❡r❣ ❇♦r❣❛♥ ❡t ❛❧ ●✐❧❞❡ ❡ ❙✉♥❞t ❆✳ ❙✐❧✈❛

      ✶ ✻✵✱✶✺✪ ✽✵✱✶✶✪ ✸✻✱✹✽✪ ✺✽✱✶✾✪ ✷ ✶✵✵✱✵✵✪ ✶✵✵✱✵✵✪ ✶✵✵✱✵✵✪ ✶✵✵✱✵✵✪ ✸ ✷✷✶✱✾✽✪ ✸✵✵✱✵✹✪ ✶✻✸✱✺✷✪ ✶✼✶✱✽✻✪ ✹ ✸✻✹✱✻✵✪ ✹✾✵✱✺✸✪ ✷✷✼✱✵✹✪ ✷✾✺✱✸✼✪ ✺ ✹✻✻✱✹✹✪ ✻✷✺✱✷✼✪ ✷✾✵✱✺✻✪ ✺✵✼✱✻✹✪ ✻ ✺✹✶✱✷✵✪ ✼✷✸✱✺✺✪ ✸✺✹✱✵✽✪ ✽✼✷✱✹✹✪

      ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ❛s ❡s❝❛❧❛s ó♣t✐♠❛s ❞❡ ♣ré♠✐♦s ❡♠ ♣❡r❝❡♥t❛❣❡♠ ❞♦ ♣ré♠✐♦ ❞❡ ❡♥tr❛❞❛✳ ❆s ❡s❝❛❧❛s ❞❡ sã♦ ♠❛✐s ❝♦♥t✐❞❛s ♥♦s ❞❡s❝♦♥t♦s ❛ ❛♣❧✐❝❛r✱ ❡ ♣❛r❛ ❛s ❝❧❛ss❡s ❛❣r❛✈❛❞❛s✱ ❡ss❛s ❞✉❛s ❡s❝❛❧❛s sã♦ ❜❛st❛♥t❡s s❡✈❡r❛s ♥♦ ♣ré♠✐♦ ❛ ❛♣❧✐❝❛r✳ ◆♦t❡✲s❡ q✉❡✱ ♣♦r ❡①❡♠♣❧♦✱ ♥❛ ❡s❝❛❧❛ ❞❡ ❜❛st❛ q✉❡ ♦ s❡❣✉r❛❞♦ ❞❡❝❧❛r❡ ✶ s✐♥✐str♦✱ ♣❛r❛ ✈❡r ♦ s❡✉ ♣ré♠✐♦ ❛❣r❛✈❛r ❡♠ ✷✵✵✪✳ ❆ ❡s❝❛❧❛ ❧✐♥❡❛r é ❛ q✉❡ ❛♣r❡s❡♥t❛ ♣ré♠✐♦s ♠❛✐s ❜❛✐①♦s ❡♠ t❡r♠♦s ❞❡ ❛❣r❛✈❛♠❡♥t♦✱ ♠❛s

      ✺✹ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ♣♦r ❞♦✐s ❛♥♦s ❝♦♥s❡❝✉t✐✈♦s✳

      ❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❝♦♠❡r❝✐❛❧✱ ♥❡♥❤✉♠❛ ❞❛s ❡s❝❛❧❛s ♦❜t✐❞❛s ♣❛r❡❝❡ s❡r ❛❝♦♥s❡❧❤á✈❡❧✱ ❞❛❞♦ q✉❡ ❛ ✈❛r✐❛çã♦ ❞♦s ♣ré♠✐♦s ❡♥tr❡ ❛s ❝❧❛ss❡s ❝♦♥s❡❝✉t✐✈❛s é ❜❛st❛♥t❡ ❡❧❡✈❛❞❛✳ ❆s ❡s❝❛❧❛s ♦❜t✐❞❛s sã♦ ❢r✉t♦ ❞❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦ ♣♦✉❝♦ ❝♦❡r❡♥t❡s ❡ ✐❧✉str❛♠ q✉❡ ❛ ❡s❝❛❧❛ ❛❝t✉❛❧ ❡stá ❛❢❛st❛❞❛ ❞♦ q✉❡ s❡r✐❛ ó♣t✐♠♦✳ ▼♦❞❡❧♦ ❆❜❡rt♦ ❆s ❡s❝❛❧❛s ❞❡ ♦❜t✐❞❛s ❛ ♣❛rt✐r ❞♦ ♠♦❞❡❧♦ ❛❜❡rt♦ ✭❚❛❜❡❧❛s ♥ã♦ sã♦ ❛❝♦♥s❡❧❤á✈❡✐s✱ ❡♠ ❛♠❜❛s ❛s ❡s❝❛❧❛s ❤á ✉♠❛ q✉❡❜r❛ ♥♦ ♣ré♠✐♦ ❞❛ ❝❧❛ss❡ ♠❛✐s ❛❣r❛✈❛❞❛✳

      ❆ ❡s❝❛❧❛ ❧✐♥❡❛r é ❛ ❡s❝❛❧❛ ♠❡♥♦s s❡✈❡r❛✱ ❡♥q✉❛♥t♦ q✉❡ ❛ ❡s❝❛❧❛ ❣❡♦♠étr✐❝❛ é ❛ q✉❡ ♣❡♥❛❧✐③❛ ♠❛✐s ♦s ✏♠❛✉s✑ ❝♦♥❞✉t♦r❡s✳

      ❆ ❡s❝❛❧❛ ❞❡ é ❛ q✉❡ ❛♣r❡s❡♥t❛ ✉♠ EQM ♠❛✐s ❡❧❡✈❛❞♦✳ ❊♠ r❡❧❛çã♦ à ❡✜❝✐ê♥❝✐❛✱ ❛ ❡s❝❛❧❛ ❞❡ ❊♠ t❡r♠♦s ❞❛ ♠❡❞✐❞❛ ❞❡ ♣❡r❞❛ ❞❡ ❡✜❝✐ê♥❝✐❛✱ ❤á ✉♠ ❣❛♥❤♦ s✐❣♥✐✜❝❛t✐✈♦ ❞❡ ❡✜❝✐ê♥❝✐❛ ❛♦ ❛❞♦♣t❛r ❛ ❡s❝❛❧❛ ❧✐♥❡❛r ♦✉ ❣❡♦♠étr✐❝❛✳

      ❊♠ t❡r♠♦s ❞❡ ♠❡❞✐❞❛s ❞❡ ❛✈❛❧✐❛çã♦ ♣r♦♣♦st❛s ♣♦r ❛ ❡s❝❛❧❛ ❧✐♥❡❛r é ❛ q✉❡ ❛♣r❡s❡♥t❛ ✉♠ RSAL ♠❛✐s ❡❧❡✈❛❞♦ ❡ ❛ ❡s❝❛❧❛ ❞❡ é ❛ q✉❡ ❛♣r❡s❡♥t❛ ♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✈❛r✐❛çã♦ ♠❛✐s ❡❧❡✈❛❞♦✱ ♥♦ ❡♥t❛♥t♦✱ ❛ ❞✐❢❡r❡♥ç❛ ❡♠ r❡❧❛çã♦ às ♦✉tr❛s ❡s❝❛❧❛s ♥ã♦ é s✐❣♥✐✜❝❛t✐✈❛✳ ❊♠ t❡r♠♦s ❞❛ ❡❧❛st✐❝✐❞❛❞❡ ❣❧♦❜❛❧✱ ❛ ❡s❝❛❧❛ ❣❡♦♠étr✐❝❛ é ❛ q✉❡ t♦r♥❛ ♦ s✐st❡♠❛ ♠❛✐s ❡❧ást✐❝♦✳

      ❚❛❜❡❧❛ ✸✳✷✻✿ ❊s❝❛❧❛s Ó♣t✐♠❛s ❡♠ P❡r❝❡♥t❛❣❡♠ ✭▼♦❞❡❧♦ ❆❜❡rt♦✮✿ ❙✳ ❆❝t✉❛❧ j ◆♦r❜❡r❣ ❇♦r❣❛♥ ❡t ❛❧ ●✐❧❞❡ ❡ ❙✉♥❞t ❆✳ ❙✐❧✈❛

      ✶ ✻✻✱✺✷✪ ✼✷✱✸✵✪ ✺✹✱✾✾✪ ✻✸✱✽✺✪ ✷ ✶✵✵✱✵✵✪ ✶✵✵✱✵✵✪ ✶✵✵✱✵✵✪ ✶✵✵✱✵✵✪ ✸ ✶✾✶✱✼✸✪ ✶✾✸✱✼✼✪ ✶✹✺✱✵✶✪ ✶✺✻✱✻✶✪ ✹ ✸✵✺✱✷✺✪ ✸✵✶✱✹✻✪ ✶✾✵✱✵✶✪ ✷✹✺✱✷✼✪ ✺ ✹✶✶✱✽✺✪ ✹✵✾✱✻✽✪ ✷✸✺✱✵✷✪ ✸✽✹✱✶✸✪ ✻ ✸✺✽✱✺✾✪ ✸✵✵✱✼✶✪ ✷✽✵✱✵✸✪ ✻✵✶✱✻✵✪

      ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ❛s ❡s❝❛❧❛s ó♣t✐♠❛s ❞❡ ♣ré♠✐♦s ❡♠ ♣❡r❝❡♥t❛❣❡♠ ❞♦ ♣ré♠✐♦ ❞❡✜♥✐❞♦ ❛ ♣r✐♦r✐✳ ❆♥❛❧✐s❛♥❞♦ ❛ ❡s❝❛❧❛ ♦❜t✐❞❛ ❡♠ ❢✉♥çã♦ ❞♦ ♣ré♠✐♦ ❞❡ ❡♥tr❛❞❛ ✭❈❧❛ss❡ ✷✮✱ ✈❡r✐✜❝❛✲s❡ ❛ ❡s❝❛❧❛ ❞❡ ❡♠ ❝♦♠♣❛r❛çã♦ ❝♦♠ ❛s ♦✉tr❛s ❡s❝❛❧❛s✱ é ❛ ♠❛✐s ❛❞❡q✉❛❞❛✱ ✈✐st♦ q✉❡ ❛s ❡s❝❛❧❛s ❞❡ ♥ã♦ ❛♣✲ r❡s❡♥t❛♠ ✉♠ ♣ré♠✐♦ q✉❡ ❛✉♠❡♥t❛ à ♠❡❞✐❞❛ q✉❡ ❛✉♠❡♥t❛ ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ ❡ ❛ ❡s❝❛❧❛ ❞❡ é ❜❛st❛♥t❡ ♣❡♥❛❧✐③❛♥t❡ ♥❛s ❝❧❛ss❡s ♠❛✐s ❛❣r❛✈❛❞❛s✱

      ✸✳✸ ❙✐st❡♠❛ ❞❡ ❇♦♥✉s ▼❛❧✉s ❆❧t❡r♥❛t✐✈♦ ♣❛r❛ ❛ ❙❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ✺✺

      

    ✸✳✸ ❙✐st❡♠❛ ❞❡ ❇♦♥✉s ▼❛❧✉s ❆❧t❡r♥❛t✐✈♦ ♣❛r❛ ❛ ❙❡✲

    ❣✉r❛❞♦r❛ ●❛r❛♥t✐❛

      ❖ s❡❣✉r♦ ♦❜r✐❣❛tór✐♦ ❞❡ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❝✐✈✐❧✱ ❡♠ ❈❛❜♦ ❱❡r❞❡✱ é r❡❣✐❞♦ ♣❡❧♦ ❉❡❝r❡t♦✲

      ♦

      ▲❡✐ ♥ ✶✼✴✷✵✵✸ ❞❡ ✶✵ ❞❡ ❋❡✈❡r❡✐r♦ ❡ ▲❡❣✐s❧❛çã♦ ❈♦♠♣❧❡♠❡♥t❛r✳ ❛♣r❡s❡♥t♦✉ ✉♠❛ ♣r♦♣♦st❛ ❛❧t❡r♥❛t✐✈❛ ❛♦ ❛❝t✉❛❧ SBM✱ ♦♥❞❡ r❡❝♦♠❡♥❞❛

      ♠❡❧❤♦r❡s ♦♣çõ❡s✱ ♥♦♠❡❛❞❛♠❡♥t❡ ❛♦ ♥í✈❡❧ ❞❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦✱ ✈✐st♦ q✉❡ ♦ s✐st❡♠❛ q✉❡ ✈✐❣♦r❛ ❛❝t✉❛❧♠❡♥t❡ ❛♣r❡s❡♥t❛ ❛❧❣✉♠❛s ❧❛❝✉♥❛s✱ ❝♦♥❢♦r♠❡ s❡ r❡❢❡r❡ ♥❛ ❙✉❜✲s❡❝çã♦

      ❊st❛ s❡❝çã♦ ♣r❡t❡♥❞❡ ❛♣r❡s❡♥t❛r ❡ ❛♥❛❧✐s❛r ❛ ♣r♦♣♦st❛ ❞❡ ❛✈❛❧✐❛♥❞♦ ♦ SBM ♣r♦♣♦st♦ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞❛s ♠❡❞✐❞❛s ❞❡ ❛✈❛❧✐❛çã♦ ♣r♦♣♦st❛s ♣♦r ❜❡♠ ❝♦♠♦ ❡st✐♠❛r ❛s ❡s❝❛❧❛s ó♣t✐♠❛s ❞❡ ♣ré♠✐♦s ❛ss♦❝✐❛❞❛s ❛ ❡st❡ ❝♦♥❥✉♥t♦ ❞❡ r❡❣r❛s ❞❡ tr❛♥s✐çã♦✳

      ◆♦ q✉❡ s❡ s❡❣✉❡✱ ❛♣r❡s❡♥t❛✲s❡ ♦ ❉❡❝r❡t♦✲❧❡✐ ♣❡❧♦ q✉❛❧ é r❡❣✐❞♦ ♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❡♠ ❈❛❜♦ ❱❡r❞❡✳

      ♦ ✸✳✸✳✶ ❉❡❝r❡t♦✲▲❡✐ ♥ ✶✼ ❞❡ ❋❡✈❡r❡✐r♦ ❞❡ ✷✵✵✸

      ♦

      ❆rt✐❣♦ ♥ ✶✼ ❙✐st❡♠❛ ❞❡ ❇♦♥✉s ▼❛❧✉s

      ❆ ❛♣ó❧✐❝❡ ✉♥✐❢♦r♠❡ ❞♦ s❡❣✉r♦ ♦❜r✐❣❛tór✐♦ ❞❡ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❝✐✈✐❧ ❛✉t♦♠ó✈❡❧ ❞❡✈❡rá ❝♦♥t❡r ✉♠❛ ❝❧á✉s✉❧❛ ❞❡ r❡❞✉çã♦ ♦✉ ❛❣r❛✈❛♠❡♥t♦ ❞♦ ♣ré♠✐♦ s✐♠♣❧❡s✱ ♣♦r ❛✉sê♥❝✐❛ ♦✉ ♥ã♦ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✱ ♥❛s ❝♦♥❞✐çõ❡s ❡st❛❜❡❧❡❝✐❞❛s ♣❡❧♦ ❇❛♥❝♦ ❞❡ ❈❛❜♦ ❱❡r❞❡✳

      ✶✳ ❖ s✐st❡♠❛ ❜♦♥✐✜❝❛❞♦ ✈✐s❛ ♣r❡♠✐❛r ♦s ❝♦♥❞✉t♦r❡s s❡♠ s✐♥✐str♦s ❞❛ s✉❛ r❡s♣♦♥s✲ ❛❜✐❧✐❞❛❞❡✱ ❛tr✐❜✉✐♥❞♦✲❧❤❡s ✉♠❛ r❡❞✉çã♦ ♥♦ ♣ré♠✐♦✳

      ♦

      ✷✳ ❖ ❇❛♥❝♦ ❞❡ ❈❛❜♦ ❱❡r❞❡✱ ❛tr❛✈és ❞♦ ❆✈✐s♦ ♥✳ ✺✴✾✽ s♦❜r❡ ❆♣ó❧✐❝❡ ❯♥✐❢♦r♠❡ ❞♦ ❙❡❣✉r♦ ❖❜r✐❣❛tór✐♦ ❞❡ ❘❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❈✐✈✐❧ ❆✉t♦♠ó✈❡❧✱ ✐♥st✐t✉✐✉ ♦ s✐st❡♠❛ ❞❡ ❛❣r❛✈❛♠❡♥t♦ ❡ ❜♦♥✐✜❝❛çã♦ ♣♦r s✐♥✐str❛❧✐❞❛❞❡✳

      ✸✳ P❛r❛ ♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ❡ ❛❣r❛✈❛♠❡♥t♦s ♣♦r s✐♥✐str♦✱ ❛♣❡♥❛s s❡rã♦ ❞❡ ❝♦♥s✐❞❡r❛r ♦s s✐♥✐str♦s q✉❡ t❡♥❤❛♠ ❞❛❞♦ ❧✉❣❛r ❛♦ ♣❛❣❛♠❡♥t♦ ❞❡ ✐♥❞❡♠♥✐③❛çã♦ ♦✉ à ❝♦♥st✐t✉✐✲ çã♦ ❞❡ ✉♠❛ ♣r♦✈✐sã♦✱ ❞❡s❞❡ q✉❡✱ ♥❡st❡ ú❧t✐♠♦ ❝❛s♦✱ ❛ s❡❣✉r❛❞♦r❛ t❡♥❤❛ ❛ss✉♠✐❞♦ ❛ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ♣❡r❛♥t❡ t❡r❝❡✐r♦s✳

      ✹✳ ❊♠ ❝❛s♦ ❞❡ ❝♦♥st✐t✉✐çã♦ ❞❡ ♣r♦✈✐sã♦✱ ❛ s❡❣✉r❛❞♦r❛ ♣♦❞❡rá s✉s♣❡♥❞❡r ❛ ❛tr✐❜✉✐çã♦ ❞❡ ❜♦♥✉s ❞✉r❛♥t❡ ♦ ♣❡rí♦❞♦ ❞❡ ❞♦✐s ❛♥♦s✱ ❞❡✈❡♥❞♦✱ ✜♥❞♦ ❡ss❡ ♣r❛③♦✱ ♦ ♠❡s♠♦ s❡r ❞❡✈♦❧✈✐❞♦ ❡ r❡♣♦st❛ ❛ s✐t✉❛çã♦ t❛r✐❢ár✐❛ s❡♠ ♣r❡❥✉í③♦ ♣❛r❛ ♦ s❡❣✉r❛❞♦✱ ❝❛s♦ ❛ s❡❣✉r❛❞♦r❛ ♥ã♦ t❡♥❤❛✱ ❡♥tr❡t❛♥t♦✱ ❛ss✉♠✐❞♦ ❛ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ♣❡r❛♥t❡ t❡r❝❡✐r♦s✱

      ♦ ♦

      ❝❢r✳ ♥✳ ✸ ❞♦ ❛rt✳ ✶✼ ❞♦ ❛✈✐s♦✳ ✺✳ ❆ ❜♦♥✐✜❝❛çã♦ é ❛♣❧✐❝á✈❡❧ ❛♦ ♣ré♠✐♦ s✐♠♣❧❡s ❛❝r❡s❝✐❞♦ ❞❡ t♦❞♦s ♦s s♦❜r❡♣ré♠✐♦s

      ✺✻ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ✻✳ P♦r ❛✉sê♥❝✐❛ ❞❡ s✐♥✐str♦ ♦ s❡❣✉r❛❞♦ t❡rá ❞✐r❡✐t♦ à r❡❞✉çã♦ ❞❡ ✸✵✪ ♥♦ ♣ré♠✐♦ s✐♠♣❧❡s q✉❛♥❞♦ ❡♠ ❞✉❛s ❛♥✉✐❞❛❞❡s ❝♦♥s❡❝✉t✐✈❛s✱ ♥ã♦ s❡ ✈❡r✐✜❝❛ ✭✐✮ ♦❝♦rrê♥❝✐❛

      ❞❡ s✐♥✐str♦ q✉❡ t❡♥❤❛ ❞❛❞♦ ❧✉❣❛r ❛♦ ♣❛❣❛♠❡♥t♦ ❞❡ q✉❛❧q✉❡r ✐♥❞❡♠♥✐③❛çã♦ ✭✐✐✮ ♦✉ ❛ ♦❝♦rrê♥❝✐❛ ❞❡ s✐♥✐str♦ q✉❡ ❞ê ❧✉❣❛r à ❝♦♥st✐t✉✐çã♦ ❞❡ ♣r♦✈✐sã♦✱ ❞❡s❞❡ q✉❡ ❛ s❡❣✉r❛❞♦r❛ t❡♥❤❛✱ ❡①♣r❡ss❛♠❡♥t❡✱ ❛❝❡✐t❡ ❛ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ♣❡r❛♥t❡ t❡r❝❡✐r♦s✳

      ✼✳ ❖❜t❡♥❞♦ ♦ s❡❣✉r❛❞♦ ✉♠❛ ❜♦♥✐✜❝❛çã♦ ♣♦r ❛✉sê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ ❞✉r❛♥t❡ ❞✉❛s ❛♥✉✐❞❛❞❡s ❝♦♥s❡❝✉t✐✈❛s✱ ❡st❛ ♥ã♦ é ❛❝✉♠✉❧á✈❡❧ ❛ ♦✉tr❛ ❜♦♥✐✜❝❛çã♦ ♣❡❧❛ ♠❛♥✉t❡♥çã♦ ❞❡ss❛ ♥ã♦ s✐♥✐str❛❧✐❞❛❞❡ ♥♦s s✉❜s❡q✉❡♥t❡s ✷ ❛♥♦s ❡ s❡❣✉✐♥t❡s✳

      ✽✳ ❖s ❝♦♥tr❛t♦s ❝♦♠ s✐♥✐str♦s s❡rã♦✱ ♥♦ ✈❡♥❝✐♠❡♥t♦ s❡❣✉✐♥t❡ à ♦❝♦rrê♥❝✐❛ ❞♦ ❢❛❝t♦✱ ♦❜r✐❣❛t♦r✐❛♠❡♥t❡ s✉❥❡✐t♦ ❛♦s s❡❣✉✐♥t❡s ❛❣r❛✈❛♠❡♥t♦s ♠í♥✐♠♦s ♥♦ ♣ré♠✐♦✿ ✭✐✮ ✶✺✪ ❡♠ ❝♦♥tr❛t♦s ❝♦♠ ✶ s✐♥✐str♦✱ ✭✐✐✮ ✸✵✪ ❡♠ ❝♦♥tr❛t♦s ❝♦♠ ✷ s✐♥✐str♦s✱ ✭✐✐✐✮ ✹✺✪ ❡♠ ❝♦♥tr❛t♦s ❝♦♠ ✸ s✐♥✐str♦s✱ ✭✐✈✮ ✶✵✵✪ ❡♠ ❝♦♥tr❛t♦s ❝♦♠ ✹ s✐♥✐str♦s✱ ✭✈✮ ❝♦♥tr❛t♦s ❝♦♠ ♠❛✐s ❞❡ ✹ s✐♥✐str♦ ♦ ❛❣r❛✈❛♠❡♥t♦ é ❢❡✐t♦ ❝❛s♦ ❛ ❝❛s♦✳ ❊st❡s ❛❣r❛✈❛♠❡♥t♦s s❡rã♦ r❡t✐r❛❞♦s ♥♦ ♣r✐♠❡✐r♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ♣ré♠✐♦ ❝♦♠ ❞✐r❡✐t♦ ❛ ❜♦♥✉s✳ ❙✐❣✲ ♥✐✜❝❛ q✉❡ ♦ ❝♦♥❞✉t♦r q✉❡ t❡♥❤❛ t✐❞♦ ✉♠ s✐♥✐str♦ ♥ã♦ só ♣❡r❞❡ ♦ ❜♦♥✉s ❞❡ ✸✵✪ q✉❡ ❧❤❡ t✐♥❤❛ s✐❞♦ ❛tr✐❜✉í❞♦✱ ❝♦♠♦ ✈ê ❛❣r❛✈❛❞♦✱ ❞❡ ✐♠❡❞✐❛t♦✱ ♦ s❡✉ ♣ré♠✐♦ ❡♠ ✶✺✪✳

      ✾✳ ➱ ✈❡❞❛❞♦ ♦ ❛❣r❛✈❛♠❡♥t♦ ❞♦ ♣ré♠✐♦ ♣♦r s✐♥✐str❛❧✐❞❛❞❡✱ q✉❡r ❤❛❥❛ ♦✉ ♥ã♦ ❧✉❣❛r ❛♦ ♣❛❣❛♠❡♥t♦ ❞❡ ✐♥❞❡♠♥✐③❛çã♦✱ s❡♠♣r❡ q✉❡ ✭✐✮ ♦ ✈❡✐❝✉❧♦ ✐♠♣❧✐❝❛❞♦ t❡♥❤❛ s✐❞♦ ♦❜❥❡❝t♦ ❞❡ ❢✉rt♦ ♦✉ r♦✉❜♦✱ r❡❣✉❧❛♠❡♥t❡ ❝♦♠✉♥✐❝❛❞♦ à ❛✉t♦r✐❞❛❞❡ ♣♦❧✐❝✐❛✐s✱ t❡♥❞♦ ♦ ❛❝✐❞❡♥t❡ t❡♥❤❛ s✐❞♦ ❞❡✈✐❞♦ ❛ ❢❛❝t♦ ♥ã♦ ✐♠♣✉tá✈❡❧ ❛♦ s❡❣✉r❛❞♦✱ r❡✈❡st✐♥❞♦✲s❡ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ❝❛s♦ ❞❡ ❢♦rç❛ ♠❛✐♦r✱ ✭✐✐✐✮ ♦ ❛❝✐❞❡♥t❡ t❡♥❤❛ s✐❞♦ ❡①❝❧✉s✐✈❛♠❡♥t❡ ❞❡✈✐❞♦ ❛ ❢❛❝t♦ ✐♠♣✉tá✈❡❧ à ✈✐t✐♠❛ ♦✉ ❛ t❡r❝❡✐r♦s✳

      ✶✵✳ ◆♦ ❝❛s♦ ❞❡ tr❛♥s❢❡rê♥❝✐❛s ❞❡ ❝♦♥tr❛t♦s ❡♥tr❡ s❡❣✉r❛❞♦r❛s ♦s ❛❣r❛✈❛♠❡♥t♦s ❡ ❜♦♥✐✜✲ ❝❛çõ❡s ❛ ❛♣❧✐❝❛r sã♦ ♠❛♥t✐❞♦s✱ r❡❢♦rç❛♥❞♦ ♦ ❧❡❣✐s❧❛❞♦r ♦ ♣r✐♥❝í♣✐♦ ❞❡ q✉❡ ♦ ❛❧✈♦ ❞❛ ♠❡❞✐❞❛ é ✉♥✐❝❛♠❡♥t❡ ♦ ❝♦♥❞✉t♦r ❤❛❜✐t✉❛❧ ❡ ♥ã♦ ♦ ✈❡í❝✉❧♦✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ♦ ❛❝✐❞❡♥t❡ ❝❛✉s❛❞♦ ♣♦r ❝♦♥❞✉t♦r ❡♠ ✈❡í❝✉❧♦ ❞❡ q✉❡ ♥ã♦ t❡♥❤❛ ❛ ❝♦♥❞✉çã♦ ❡❢❡❝✲ t✐✈❛ ♣❡♥❛❧✐③❛ ♦ ❝♦♥❞✉t♦r t✐t✉❧❛r ❞♦ ✈❡í❝✉❧♦✱ ❝♦♠♦ s❡ ❞❡st❡ s❡ tr❛t❛ss❡✳ ➱ ♦ ❝❛s♦ ❞♦ ♣r♦♣r✐❡tár✐♦ ❞❛r ❞❡ ❡♠♣rést✐♠♦ ♦ s❡✉ ✈❡í❝✉❧♦ ❛ ✉♠ ❛♠✐❣♦ q✉❡ ❧❤❡ ✐rá ❢❛③❡r ❞❡t❡r♠✐♥❛❞❛ t❛r❡❢❛ ❛ tít✉❧♦ ❣r❛t✉✐t♦✳

      ✸✳✸✳✷ ❈rít✐❝❛s ❡ Pr♦♣♦st❛s ❛♣r❡s❡♥t❛s ♣♦r ❖sór✐♦

      ❈❛❞❛ ✉♠ ❞♦s ♣♦♥t♦s ❛ s❡❣✉✐r r❡❢❡r❡♥❝✐❛❞♦s✱ ❢♦r❛♠ r❡ss❛❧t❛❞♦s ♣♦r ❚❡♠♦s r❡s❡r✈❛s s♦❜r❡ ❛ ✏❥✉st❡③❛✑ ❞❛s s♦❧✉çõ❡s ♣r❡❝♦♥✐③❛❞❛s ♣❡❧♦ ❧❡❣✐s❧❛❞♦r✱ ♣♦r✲

    • q✉❛♥t♦ ✈❡r✐✜❝❛♠♦s q✉❡ ❡st❡ r❡❣✐♠❡ ♥ã♦ ❞✐st✐♥❣✉❡ ♦ ❝❛s♦ ❞❡ ✉♠❛ ❛♣ó❧✐❝❡ ❝♦♠ ♥♦✈❡ ❛♥♦s s❡♠ s✐♥✐str♦ ✭q✉❡ ❝♦♠ ♦ ♣r✐♠❡✐r♦ s✐♥✐str♦ ♣❡r❞❡ ❛ ❜♦♥✐✜❝❛çã♦ ❡ é ❛❣r❛✈❛❞♦ ❛✉t♦♠❛t✐❝❛♠❡♥t❡ ❡♠ ✶✺✪✮ ❞❛ ❛♣ó❧✐❝❡ ❝♦♠ ✉♠ ❛♥♦ s❡♠ s✐♥✐str♦✱ q✉❡ t❡rá ♦ ♠❡s♠♦
    • ❉❡❢❡♥❞❡♠♦s q✉❡ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦ ❡s❝❛❧ã♦ ❞❡ ❇♦♥✉s✴❆❣r❛✈❛♠❡♥t♦ ❞❡✈❡r✐❛ ❛t❡♥❞❡r✲s❡ ❛♦ ❤✐stór✐❝♦ ❞❡ ❜♦♥✉s✲❛❣r❛✈❛♠❡♥t♦ ❞❛ ❛♣ó❧✐❝❡✱ ❡ ♥ã♦ ❛♣❡♥❛s ♦ ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s ❞❛ ❛♥✉✐❞❛❞❡ ❡ ♦ ♥ú♠❡r♦ ❞❡ ❛♥♦s s❡♠ s✐♥✐str♦s✳ ❖✉tr❛ ❝rít✐❝❛ ♣r❡♥❞❡✲ s❡ ❝♦♠ ♦s ❝❛s♦s ❞❡ ♣❡r❞❛ t♦t❛❧ ❡♠ q✉❡ ❛ ❛♣ó❧✐❝❡ é ❛♥✉❧❛❞❛✳ ❈♦♠ ❛ ❡❢❡❝t✐✈❛çã♦ ❞❡ ✉♠ ♥♦✈♦ ❝♦♥tr❛t♦✱ ❛ ♥♦✈❛ ❛♣ó❧✐❝❡ ✐♥✐❝✐❛✲s❡ s❡♠ ❛❣r❛✈❛♠❡♥t♦ ♣♦rq✉❡ s❡ tr❛t❛ ❞❡ ✉♠ ♥♦✈♦ ❝♦♥tr❛t♦✳ ◗✉❡st✐♦♥❛✲s❡ ❛té q✉❡ ♣♦♥t♦ ♥ã♦ ❞❡✈❡r✐❛ ❛ ❛♣ó❧✐❝❡ ✐♥✐❝✐❛r ❝♦♠

    • P❛r❛ r❡s♦❧✈❡r ❛s ❧❛❝✉♥❛s ❛♣r❡s❡♥t❛❞❛s✱ s✉❣❡r✐♠♦s ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❡ ✉♠ ❡sq✉❡♠❛ ❞❡ ❆❣r❛✈❛♠❡♥t♦✴❇♦♥✐✜❝❛çã♦ q✉❡ ❢✉♥❝✐♦♥❡ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿

      ❙❡ ♥ã♦ t✐✈❡r s✐♥✐str♦ ❝♦♠ ❝✉❧♣❛ ♥❛ ❛♥✉✐❞❛❞❡✿ ·

      ✸✳✸✳✸ ❉❡✜♥✐çã♦ ❞♦ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦

      ∗ ❙❡ ❝♦♥s✐❞❡r❛r♠♦s α = 2✱ ♦ s✐♥✐str♦ t❡♠ ♦ ❞♦❜r♦ ❞♦ ♣❡s♦ ❞♦ ♥ú♠❡r♦ ❞❡ ❛♥♦s s❡♠ s✐♥✐str♦ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦ ❊s❝❛❧ã♦❀

      ❙❡ ❝♦♥s✐❞❡r❛r♠♦s α = 1✱ ♦ s✐♥✐str♦ t❡♠ ♦ ♠❡s♠♦ ♣❡s♦ ❞♦ ♥ú♠❡r♦ ❞❡ ❛♥♦s s❡♠ s✐♥✐str♦ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦ ❊s❝❛❧ã♦❀

      ✕ ❉❡✈❡♠♦s ♣❡♥s❛r ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞❡ α✳ P♦r ❡①❡♠♣❧♦✿ ∗

      ◆♦✈♦ ❊s❝❛❧ã♦ ❂ ❊s❝❛❧ã♦ ❆♥t❡r✐♦r ✰ αn ✭❛❣r❛✈❛♠❡♥t♦✮ ✭n = ♥ú♠❡r♦ ❞❡ s✐♥✐str♦s ❞✉r❛♥t❡ ❛ ❛♥✉✐❞❛❞❡✮ ✭α = ♣❡s♦ ❞♦ s✐♥✐str♦ ♥❛ ❞❡t❡r♠✐✲ ♥❛çã♦ ❞♦ ❊s❝❛❧ã♦✮

      ❙❡ t✐✈❡r n s✐♥✐str♦s ❝♦♠ ❝✉❧♣❛ ♥❛ ❛♥✉✐❞❛❞❡✿ ·

      ◆♦✈♦ ❊s❝❛❧ã♦ ❂ ❊s❝❛❧ã♦ ❆♥t❡r✐♦r ✲✶ ✭❜♦♥✐✜❝❛çã♦✮ ∗

      ❢♦r♠❛✿ ∗

      ✸✳✸ ❙✐st❡♠❛ ❞❡ ❇♦♥✉s ▼❛❧✉s ❆❧t❡r♥❛t✐✈♦ ♣❛r❛ ❛ ❙❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ✺✼

      ✕ ❉❡t❡r♠✐♥❛❞❛ ❛ ♣❡r❝❡♥t❛❣❡♠ ❞❡ ❆❣r❛✈❛♠❡♥t♦✴❇♦♥✐✜❝❛çã♦ s♦❜r❡ ♦ ♣ré♠✐♦ s✐♠♣❧❡s ❛tr❛✈és ❞✉♠❛ t❛❜❡❧❛ ❞❡ ❝♦rr❡s♣♦♥❞ê♥❝✐❛❀ ✕ ◆♦ ✜♠ ❞❡ ❝❛❞❛ ❛♥✉✐❞❛❞❡ ❞❛ ❛♣ó❧✐❝❡ ♦ ❊s❝❛❧ã♦ é ❞❡t❡r♠✐♥❛❞♦ ❞❛ s❡❣✉✐♥t❡

      ✕ ❉❡t❡r♠✐♥❛ ♦ ♥í✈❡❧ ❞❡ r✐s❝♦ ❞♦s ❝♦♥❞✉t♦r❡s ❤❛❜✐t✉❛✐s ❞✉♠❛ ❛♣ó❧✐❝❡ ❡ ♥ã♦ ♥❡❝❡ss❛r✐❛♠❡♥t❡ ❞♦ t✐t✉❧❛r✳ ❉❡st❛ ❢♦r♠❛✱ s❡ ♦ t✐t✉❧❛r t✐✈❡r ✈ár✐❛s ❛♣ó❧✐❝❡s✱ s♦♠❡♥t❡ ❛ ❛♣ó❧✐❝❡ ❝♦♠ s✐♥✐str♦ é ❛❣r❛✈❛❞❛❀

      ✕ ❈❛❞❛ ❛♣ó❧✐❝❡ t❡♠ ✉♠ ❡ ✉♠ só ❊s❝❛❧ã♦ ♣♦r ❛♥✉✐❞❛❞❡✱ ♥ã♦ s❡♥❞♦ ❛ss♦❝✐❛❞♦ ❛ ✉♠ r✐s❝♦ ❡♠ ♣❛rt✐❝✉❧❛r❀

      ∗ ✵ ⇒ ❙✐t✉❛çã♦ ◆♦r♠❛❧

      ∗ ❱❛❧♦r ♣♦s✐t✐✈♦ ⇒ ❛❣r❛✈❛♠❡♥t♦

      ∗ ❱❛❧♦r ♥❡❣❛t✐✈♦ ⇒ ❜♦♥✐✜❝❛çã♦

      ✕ ❋✉♥❝✐♦♥❡ ❞❡ ❢♦r♠❛ ❧✐♥❡❛r ✉t✐❧✐③❛♥❞♦ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❊s❝❛❧ã♦❀ ✕ ❊s❝❛❧ã♦ é ✉♠ ✈❛❧♦r ♥✉♠ér✐❝♦ ✐♥t❡✐r♦ ✭✳ ✳ ✳ ✱✲✹✱✲✸✱✲✷✱✲✶✱✵✱✰✶✱✰✷✱✰✸✱✰✹✱✳ ✳ ✳ ✮❀

      ❛❣r❛✈❛♠❡♥t♦✳

      ❉❛ ♣r♦♣♦st❛ ❛❝✐♠❛ ❛♣r❡s❡♥t❛❞❛✱ ❝♦♠ ❛s ❞❡✈✐❞❛s ❛❞❛♣t❛çõ❡s✱ ❛♥❛❧✐s❛r❡♠♦s ♦ s✐st❡♠❛

    • ❖ ♣❡s♦ à ❛tr✐❜✉✐r ❛ ❝❛❞❛ s✐♥✐str♦ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛ ❝❧❛ss❡ é ❞❛❞♦ ♣♦r α = 1❀
    • ❖ ❝♦♥❝❡✐t♦ ❊s❝❛❧ã♦ é s✉❜st✐t✉í❞♦ ♣♦r ❈❧❛ss❡✱ ♦♥❞❡ é ❞❡✜♥✐❞❛ ♣♦r ♦r❞❡♠ ❝r❡s❝❡♥t❡ ❞❡ ♣r♦♣❡♥sã♦ à s✐♥✐str❛❧✐❞❛❞❡✱ s❡♥❞♦ q✉❡ ♥♦ t♦t❛❧ s❡rã♦ ✻ ❡ ❛ ❡♥tr❛❞❛ ♥♦ s✐st❡♠❛ ❢❛r✲s❡✲á✱ ❣❡r❛❧♠❡♥t❡✱ ♣❡❧❛ ❈❧❛ss❡ ✷❀
    • ❘❡❣r❛ ❞❡ ❚r❛♥s✐çã♦✿ P♦r ❝❛❞❛ ❛♥♦ s❡♠ s✐♥✐str♦✱ ❞❡s❝✐❞❛ ❞❡ ✉♠❛ ❝❧❛ss❡✱ ❡ ♣♦r ❝❛❞❛ s✐♥✐str♦ ❝♦♠ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡✱ ♠❡s♠♦ ♣❛r❝✐❛❧✱ s✉❜✐❞❛ ❞❡ ✉♠❛ ❝❧❛ss❡✳

      6 ¯

      ✸✳✸✳✹ ❉✐str✐❜✉✐çã♦ ▲✐♠✐t❡✿ ❈❛rt❡✐r❛ ❋❡❝❤❛❞❛

      ❖ s✐st❡♠❛ ❛ss✐♠ ❞❡✜♥✐❞♦ é r❡♣r❡s❡♥t❛❞♦ ♣♦r ✉♠❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈✱ s❡♠ q✉❡ s❡❥❛ ♥❡❝❡ssár✐♦ ❡❢❡❝t✉❛r ❛❧t❡r❛çõ❡s✳

      − {0} − {1} {2} {3, 4, . . .} − − {0} − {1} {2, 3, . . .} − − − {0} − {1, 2, . . .} − − − − {0} {1, 2, . . .} .

      6 {0} {1} {2} {3} {4} {5, 6, . . .} {0} − {1} {2} {3} {4, 5, . . .}

      5

      4

      3

      2

      1

      T =

      5

      ✺✽ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛

      4

      3

      2

      1

      ♣♦r✿

      T ✱ é ❞❛❞❛

      ✭✸✳✷✼✮ ❈♦♠ ❛s ❞❡✜♥✐çõ❡s ❛❝✐♠❛✱ t❡♠✲s❡ q✉❡ ❛ ♠❛tr✐③ ❞❛s r❡❣r❛s ❞❡ tr❛♥s✐çõ❡s✱ ¯

      ❖ q✉❡ ❡q✉✐✈❛❧❡ ❛ ✉♠ ✈❡❝t♦r ❞❡ ♣ré♠✐♦s ❞❡ ¯ b T = (70 100 115 130 145 200).

      ❈❧❛ss❡ ❉❡s❝♦♥t♦✴❆❣r❛✈❛♠❡♥t♦ ✶ ✸✵✪ ❉❡s❝♦♥t♦ ✷ ✵✪❉❡s❝♦♥t♦ ✸ ✶✺✪ ❆❣r❛✈❛♠❡♥t♦ ✹ ✸✵✪ ❆❣r❛✈❛♠❡♥t♦ ✺ ✹✺✪ ❆❣r❛✈❛♠❡♥t♦ ✻ ✶✵✵✪ ❆❣r❛✈❛♠❡♥t♦

      ❆s ❝❧❛ss❡s ❞♦ s✐st❡♠❛s ❞❡ ❜♦♥✉s s❡rã♦ ❞❡✜♥✐❞❛s ♥❛ ❚❛❜❡❧❛ ❚❛❜❡❧❛ ✸✳✷✼✿ ❈❧❛ss❡s ❞♦ ❙✐st❡♠❛ ❞❡ ❜♦♥✉s ❛❧t❡r♥❛t✐✈♦

      ❆ ♠❛tr✐③ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ tr❛♥s✐çã♦ ♣❛r❛ ♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❞❡✜♥✐❞♦ ♥❛

      ✸✳✸ ❙✐st❡♠❛ ❞❡ ❇♦♥✉s ▼❛❧✉s ❆❧t❡r♥❛t✐✈♦ ♣❛r❛ ❛ ❙❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ✺✾  P

      1

      2

      3

      4

      5

      6 4  p p p p p 1 − p 1   1 2 3 4 i P 3 i=0 2 p p p p 1 − p     1 2 3 i P 2 i=0

      3   p p p 1 − p 1 2 i i=0 P ¯ = T P   1 .

      4     p p 1 − p 1 i i=0

      5 p 1 − p 6 p 1 − p

      ❆♥❛❧✐s❛♥❞♦ ❛ ♠❛tr✐③ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ tr❛♥s✐çã♦✱ ❝♦♥❝❧✉✐✲s❡ q✉❡ ❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈ ✐♠♣❧í❝✐t❛ ♥♦ ♠♦❞❡❧♦ é ✐rr❡❞✉tí✈❡❧✱ ✐st♦ é✱ t♦❞❛s ❛s ❝❧❛ss❡s ❝♦♠✉♥✐❝❛♠ ❡♥tr❡ s✐✳ ❆ ❝❛❞❡✐❛ é ✜♥✐t❛ ❡ ❛♣❡r✐ó❞✐❝❛✱ ♣♦rt❛♥t♦✱ é r❡❝♦rr❡♥t❡ ♣♦s✐t✐✈❛✱ ♣❡❧♦ q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ ❝♦✐♥❝✐❞✐rá ❝♦♠ ❛ ❞✐str✐❜✉✐çã♦ ❡st❛❝✐♦♥ár✐❛✳

      ❚❛❜❡❧❛ ✸✳✷✽✿ ❉✐str✐❜✉✐çã♦ ▲✐♠✐t❡ ❡ P♦♥❞❡r❛❞❛ ♥♦ ▼✳ ❋❡❝❤❛❞♦✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦ j ❉✐str✐❜✉✐çã♦ ▲✐♠✐t❡ ❉✐str✐❜✉✐çã♦ P♦♥❞❡r❛❞❛

      ✶ ✵✱✽✷✶✼✺✺✷✺✹ ✵✱✽✷✾✸✶✶✽✵✹✵✸ ✷ ✵✱✵✼✻✸✵✵✺✸✾ ✵✱✵✼✻✾✵✷✺✾✶✹✼ ✸ ✵✱✵✸✶✽✸✹✺✽✽ ✵✱✵✸✼✻✵✼✹✵✾✼ ✹ ✵✱✵✷✶✾✹✾✷✹✸ ✵✱✵✷✵✽✹✾✺✻✵✾ ✺ ✵✱✵✷✶✸✻✾✶✹✶ ✵✳✵✶✻✺✵✻✹✾✵✵ ✻ ✵✱✵✷✻✼✾✶✷✸✻ ✵✱✵✶✽✽✷✷✶✹✹✾

      ❚♦t❛❧ ✶ ✶ ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ❛s ❞✐str✐❜✉✐çõ❡s ❧✐♠✐t❡ ❡ ♣♦♥❞❡r❛❞❛ ♣❛r❛ ✉♠ s❡❣✉r❛❞♦ r❡t✐✲ r❛❞♦ ❛♦ ❛❝❛s♦ ❞❛ ❝❛rt❡✐r❛ ❞❡ ❛♣ó❧✐❝❡s✳ P❛r❛ ❛s ❞✉❛s ❞✐str✐❜✉✐çõ❡s ♦❜t✐❞❛s ✈❡r✐✜❝❛✲s❡ q✉❡

      ❡①✐st✐rá ✉♠❛ ❣r❛♥❞❡ ❛❣❧♦♠❡r❛çã♦ ❞❡ ❛♣ó❧✐❝❡s ♥❛ ❝❧❛ss❡ ❜♦♥✐✜❝❛❞❛ ❞♦ s✐st❡♠❛ ✭❈❧❛ss❡ ✶✮✳ ❖ ♣ré♠✐♦ ♠é❞✐♦ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡ ❡ ♥ã♦ ❡st❛❝✐♦♥❛r✐❞❛❞❡ é✱ r❡s♣❡❝✲ t✐✈❛♠❡♥t❡✱ ✽✵✱✶✷✪ ❡ ✼✽✱✾✻✪ ❞♦ ♣ré♠✐♦ ❞❡ ❡♥tr❛❞❛✳

      ❆♥❛❧✐s❛♥❞♦ ❛ ❋✐❣✉r❛ ♦♥❞❡ ✐❧✉str❛ ❛ ❡✈♦❧✉çã♦ ❞♦ ♣ré♠✐♦ ❞❡ ✉♠ ♥♦✈♦ s❡❣✉r❛❞♦✱

      ♦

      ✈❡r✐✜❝❛✲s❡ q✉❡ ♦ ♣ré♠✐♦ ♠é❞✐♦ ♦s❝✐❧❛ ♥♦s ✸ ♣r✐♠❡✐r♦s ❛♥♦s✱ s❡♥❞♦ q✉❡ ♥♦ ✶ ❛♥♦ ♦ ♣ré♠✐♦

      ♦

      ♠é❞✐♦ é ♠❛✐s ❜❛✐①♦ q✉❡ ♥♦s r❡st❛♥t❡s ❛♥♦s✳ ❆ ♣❛rt✐r ❞♦ ✸ ❛♥♦ ♦ ♣ré♠✐♦ ✈❛✐ ❛✉♠❡♥t❛♥❞♦✱

      ♦

      s❡♥❞♦ q✉❡ ❡st❛❜✐❧✐③❛ ❛ ♣❛rt✐r ❞♦ ✶✺ ❛♥♦✱ ♥♦ ❡♥t❛♥t♦ ♥ã♦ ❛t✐♥❣❡ ❛ ❡st❛❝✐♦♥❛r✐❞❛❞❡ ♥❡ss❡s ✷✵ ❛♥♦s✳

      ✸✳✸✳✺ ❉✐str✐❜✉✐çã♦ ▲✐♠✐t❡✿ ❈❛rt❡✐r❛ ❆❜❡rt❛

      ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ♦ ✈❡❝t♦r ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ ✉♠ ♥♦✈♦ s❡❣✉r❛❞♦ s❡r ❝♦❧♦❝❛❞♦ ♥✉♠❛ ❞❛s s ❝❧❛ss❡s ❞♦ s✐st❡♠❛✳ ❋♦✐ ❡st✐♠❛❞♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦s ❞❛❞♦s ❞❛ ❝❛rt❡✐r❛✱ ❞❡ ❢♦r♠❛ ❛♥á❧♦❣❛ ❛♦ ♦✉tr♦ ♠♦❞❡❧♦ ✭♠♦❞❡❧♦ q✉❡ ✈✐❣♦r❛ ❛❝t✉❛❧♠❡♥t❡ ♥❛ s❡❣✉r❛❞♦r❛

      ✻✵ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❋✐❣✉r❛ ✸✳✶✸✿ ❊✈♦❧✉çã♦ ❞♦ Pré♠✐♦ ▼é❞✐♦ ✭▼♦❞❡❧♦ ❋❡❝❤❛❞♦✮✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦

      ❚❛❜❡❧❛ ✸✳✷✾✿ Pr♦❜❛❜✐❧✐❞❛❞❡s ❞❡ ❊♥tr❛❞❛s ♥❛s ❈❧❛ss❡s✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦ j ✶ ✷ ✸ ✹ ✺ ✻ c (j)

      ✵✱✶✵✻✹✸✶✶✽ ✵✱✽✽✸✸✺✶✵✺✻ ✵✱✵✵✽✷✷✾✻✾✷ ✵✱✵✵✶✺✼✶✾✻✹ ✵✱✵✵✵✶✽✹✾✸✼ ✵✱✵✵✵✷✸✶✶✼✶ ❆♥❛❧✐s❛♥❞♦ ❛ ❚❛❜❡❧❛ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ♠❛✐♦r ♣❛rt❡ ❞♦s s❡❣✉r❛❞♦s ❡♥tr❛r❛♠

      ♣❛r❛ ❛ ❝❧❛ss❡ ❞❡ ❡♥tr❛❞❛ ✭❈❧❛ss❡ ✷✮✱ ♣♦rt❛♥t♦✱ ❣❡r❛❧♠❡♥t❡ ❛ ❝❧❛ss❡ ❞❡ ❡♥tr❛❞❛ é r❡s♣❡✐✲ t❛❞❛ ♣❡❧❛ ❙❡❣✉r❛❞♦r❛✳ ❱❡r✐✜❝❛✲s❡ ❛✐♥❞❛✱ q✉❡ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ♥♦✈♦ s❡❣✉r❛❞♦ s❡r ❝♦❧♦❝❛❞♦ ♥❛s ❝❧❛ss❡s ❛❣r❛✈❛❞❛s ❞♦ s✐st❡♠❛ é ❜❛st❛♥t❡ ❜❛✐①❛✳ ■st♦ ♣♦❞❡ ❞❡✈❡r✲s❡ ❛♦ ❢❛❝t♦ ❞❡ ❛s s❡❣✉r❛❞♦r❛s ♥ã♦ ❡①✐❣✐r❡♠ ❛ ❛♣r❡s❡♥t❛çã♦ ❞♦ ❝❡rt✐✜❝❛❞♦ ❞❡ t❛r✐❢❛çã♦ ♦✉ ❛✐♥❞❛ ♣♦r q✉❡stõ❡s ❝♦♠❡r❝✐❛✐s✳

      ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ❛ ❡st✐♠❛t✐✈❛ ❞♦ ✈❡❝t♦r ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ s❛í❞❛ ❞❡ ✉♠ s❡❣✉r❛❞♦ ♣❛r❛ ❝❛❞❛ ✉♠❛ ❞❛s ✻ ❝❧❛ss❡s ❞♦ s✐st❡♠❛✳ ❚❛❜❡❧❛ ✸✳✸✵✿ Pr♦❜❛❜✐❧✐❞❛❞❡s ❞❡ ❙❛í❞❛✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦ j

      ✶ ✷ ✸ ✹ ✺ ✻ q (j) ✵✱✷✺✾✶✽✽✽✸✾ ✵✱✾✺✾✷✸✼✻✵✷ ✵✱✸✼✺✾✷✽✺✺✸ ✵✱✸✽✼✽✵✽✷✼✶ ✵✱✹✹✹✺✷✵✾✽✸ ✵✱✾✸✼✺

      ❆♥❛❧✐s❛♥❞♦ ❛ ❚❛❜❡❧❛ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ s❛í❞❛ ♥❛ ❝❧❛ss❡ ❞❡ ❡♥tr❛❞❛ é ❡♥♦r♠❡ ✭❈❧❛ss❡ ✷✮✱ q✉❡stã♦ ❡st❛ ❥á ❛♥t❡r✐♦r♠❡♥t❡ ❥✉st✐✜❝❛❞❛ ♣❡❧❛ ❧❡❣✐s❧❛çã♦ ❞❡ ❈❛❜♦ ❱❡r❞❡✳ ◆♦ ❡♥t❛♥t♦ ✈❡r✐✜❝❛✲s❡ q✉❡✱ à ❡①❝❡♣çã♦ ❞❛ ❈❧❛ss❡ ✷✱ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ s❛í❞❛ ❞❡ ✉♠ s❡❣✉r❛❞♦ ❞♦ s✐st❡♠❛ é ♠❛✐♦r à ♠❡❞✐❞❛ q✉❡ ❛✉♠❡♥t❛♠ ♦s ❛❣r❛✈❛♠❡♥t♦s ❛ ❛♣❧✐❝❛r ❛♦ ♣ré♠✐♦✱ s❡♥❞♦ q✉❡ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ s❡❣✉r❛❞♦ ❛❜❛♥❞♦♥❛r ❛ ❙❡❣✉r❛❞♦r❛✱ s❛❜❡♥❞♦ q✉❡ ❡stá ♥❛ ❝❧❛ss❡ ♠❛✐s ❛❣r❛✈❛❞❛ ✭❈❧❛ss❡ ✻✮✱ é ♠✉✐t♦ ❡❧❡✈❛❞❛✳

      ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ❛s ❞✐str✐❜✉✐çõ❡s ❧✐♠✐t❡ ❡ ♣♦♥❞❡r❛❞❛ ❞❡ ✉♠ s❡❣✉r❛❞♦ r❡t✐r❛❞♦ ❛♦ ❛❝❛s♦ ❞♦ s✐st❡♠❛ ❡st❛r ❡♠ ✉♠❛ ❞❛s ✻ ❝❧❛ss❡s ❞♦ s✐st❡♠❛✳ ❆♥❛❧✐s❛♥❞♦ ♦s r❡s✉❧t❛❞♦s

      ✸✳✸ ❙✐st❡♠❛ ❞❡ ❇♦♥✉s ▼❛❧✉s ❆❧t❡r♥❛t✐✈♦ ♣❛r❛ ❛ ❙❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ✻✶ ❚❛❜❡❧❛ ✸✳✸✶✿ ❉✐str✐❜✉✐çã♦ ▲✐♠✐t❡ ❡ P♦♥❞❡r❛❞❛ ✭▼✳ ❆❜❡rt♦✮✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦ j

      ❉✐str✐❜✉✐çã♦ ▲✐♠✐t❡ ❉✐str✐❜✉✐çã♦ P♦♥❞❡r❛❞❛ ✶ ✵✱✸✶✷✺✺✻✶ ✵✱✷✻✽✸✷✹✺ ✷ ✵✱✻✻✽✻✶✼✽ ✵✱✼✶✸✽✾✼✾ ✸ ✵✱✵✶✷✾✾✵✶ ✵✱✵✶✷✺✽✺✶ ✹ ✵✱✵✵✸✽✺✺✵ ✵✱✵✵✸✺✷✷✺ ✺ ✵✱✵✵✶✶✾✹✻ ✵✱✵✵✶✵✵✾✸ ✻ ✵✱✵✵✵✼✽✻✺ ✵✱✵✵✵✻✻✵✻

      ❚♦t❛❧ ✶ ✶ tr❛rã♦ ♥❛ ❝❧❛ss❡ ❞❡ ❡♥tr❛❞❛ ✭❈❧❛ss❡ ✷✮ ❡ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠❛ ❛♣ó❧✐❝❡ s❡ ❡♥❝♦♥tr❛r ♥❛s ❝❧❛ss❡s ❛❣r❛✈❛❞❛s é ♠✉✐t♦ ❜❛✐①❛✳ ❖ ♣ré♠✐♦ ♠é❞✐♦✱ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡ ❡ ♥ã♦ ❡st❛❝✐♦♥❛r✐❞❛❞❡ é✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ✾✶✱✵✺✪ ❡ ✾✷✱✸✸✪✱ ❞♦ ♣ré♠✐♦ ❞❡✜♥✐❞♦ ❛ ♣r✐♦r✐✳

      ❆♥❛❧✐s❛♥❞♦ ❛ ❋✐❣✉r❛ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦ ♣ré♠✐♦ ♠é❞✐♦ ✈❛✐ ❞✐♠✐♥✉✐♥❞♦ ❛♦ ❧♦♥❣♦

      ♦

      ❞♦s ❛♥♦s✱ ❡st❛❜✐❧✐③❛♥❞♦ ❛♦ ✜♠ ❞♦s ✶✺ ❛♥♦✱ ♥ã♦ ❛t✐♥❣✐♥❞♦✱ ♥♦ ❡♥t❛♥t♦✱ ❛ ❡st❛❝✐♦♥❛r✐❞❛❞❡ ❛♦ ❧♦♥❣♦ ❞❡ss❡s ✷✵ ❛♥♦s✳

      ❋✐❣✉r❛ ✸✳✶✹✿ ❊✈♦❧✉çã♦ ❞♦ P M ♥♦ ▼♦❞❡❧♦ ❆❜❡rt♦✿ ❙✳❆❧t❡r♥❛t✐✈♦ ❈♦♠♣❛r❛♥❞♦ ❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ ♦❜t✐❞❛ ❡♥tr❡ ♦s ❞♦✐s ♠♦❞❡❧♦s ❡st✉❞❛❞♦s✱ ✈❡r✐✜❝❛✲ s❡ q✉❡✱ ❡♥q✉❛♥t♦ q✉❡ ♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ❡st✐♠❛ q✉❡ ❡①✐st✐rá ✉♠❛ ❣r❛♥❞❡ ❛❣❧♦♠❡r❛çã♦

      ❞❡ ❛♣ó❧✐❝❡s ♥❛ ❝❧❛ss❡ ❜♦♥✐✜❝❛❞❛ ❞♦ s✐st❡♠❛✱ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦ ❡①✐st✐rá ✉♠❛ ❣r❛♥❞❡ ❛❣❧♦♠❡r❛çã♦ ❞❡ ❛♣ó❧✐❝❡s ♥❛ ❝❧❛ss❡ ❞❡ ❡♥tr❛❞❛ ❞♦ s✐st❡♠❛✱ t❛❧ ❝♦♠♦ ❛❝♦♥t❡❝❡ ❛❝t✉❛❧♠❡♥t❡ ♥❛ ❝❛rt❡✐r❛ ❞❛ ●❛r❛♥t✐❛✱ ❙✳❆✳ ■st♦ ❥✉st✐✜❝❛✲s❡ ♣♦rq✉❡ ♦ ♠♦❞❡❧♦ ❛❜❡rt♦ ❝♦♥s✐❞❡r❛ ❛s ❡♥tr❛❞❛s ❡ s❛í❞❛s ❞❡ ❛♣ó❧✐❝❡s ♥♦ s✐st❡♠❛✳ ❊♠ ❛♠❜♦s ♦s ♠♦❞❡❧♦s ❡st✐♠❛✲s❡ q✉❡ ❛ ♠❛✐♦r ♣❛rt❡ ❞♦s s❡❣✉r❛❞♦s s❡ ❡♥❝♦♥tr❛rã♦ ♥❛s ❝❧❛ss❡s ♥ã♦ ❛❣r❛✈❛❞❛s ❞♦ s✐st❡♠❛✳

      ✸✳✸✳✻ ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s

      ❆ ❚❛❜❡❧❛ ❜❡♠ ❝♦♠♦

      ✻✷ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❚❛❜❡❧❛ ✸✳✸✷✿ ❊s❝❛❧❛ ❞❡ P▼✱ ❊◗▼ ❡ ▼❡❞✐❞❛ ❞❡ ❊✜❝✐ê♥❝✐❛✿ ❙✳ ❆❧t❡r♥❛t✐✈♦

      ❊s❝❛❧❛ ❞❡ ◆♦r❜❡r❣ ❊s❝❛❧❛ ❞❡ ❇♦r❣❛♥ ❡t ❛❧ ❈❧❛ss❡ ▼✳ ❋❡❝❤❛❞♦ ▼✳ ❆❜❡rt♦ ▼✳ ❋❡❝❤❛❞♦ ▼✳ ❆❜❡rt♦

      ✶ ✵✱✵✽✷✶✹✼ ✵✱✶✵✸✹✽✽ ✵✱✵✽✽✵✸✽ ✵✱✶✵✾✹✾✶ ✷ ✵✱✷✹✻✵✽✾ ✵✱✶✺✽✼✻✺ ✵✱✷✻✹✵✾✷ ✵✱✶✺✸✾✼✶ ✸ ✵✱✸✾✻✶✺✶ ✵✱✷✽✽✷✹✶ ✵✱✹✵✸✶✸✸ ✵✱✷✼✶✺✶✶ ✹ ✵✱✺✸✸✵✾✻ ✵✱✹✶✼✺✸✹ ✵✱✺✸✾✹✺✵ ✵✱✸✾✹✸✾✽ ✺ ✵✱✻✺✽✶✾✾ ✵✱✺✼✽✵✹✾ ✵✱✻✺✾✽✷✽ ✵✱✺✺✾✹✷✵ ✻ ✵✱✼✻✶✷✹✵ ✵✱✼✼✾✽✼✷ ✵✱✼✻✻✽✻✷ ✵✱✺✽✶✶✶✶

      P M ✵✱✶✹✺✵✺✹ ✵✱✶✹✺✶✺✼ ✵✱✶✹✺✵✺✹ ✵✱✶✹✺✵✺✹ e(∆) ✵✱✵✹✻✶✽✸ ✵✱✵✷✷✼✸✹ ✵✱✵✹✷✷✷✻ ✵✱✵✷✷✶✺✻

      EQM ✵✱✵✷✽✹✷✵ ✵✱✵✸✾✾✽✾ ✵✱✵✷✶✺✷✷ ✵✱✵✹✶✺✾✷

      ❆♥❛❧✐s❛♥❞♦ ❛ ❡s❝❛❧❛ ❞❡ ♦❜t✐❞❛✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ♥❛ ❝❧❛ss❡ ❜♦♥✐✜❝❛❞❛ ✭❈❧❛ss❡ ✶✮ ❡ ♥❛ ❝❧❛ss❡ ♠❛✐s ❛❣r❛✈❛❞❛ ✭❈❧❛ss❡ ✻✮ ♦ ♣ré♠✐♦ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ é ✐♥❢❡r✐♦r ❛♦ ❛❜❡rt♦✱ ❡♥q✉❛♥t♦ q✉❡ ♥❛s ♦✉tr❛s ❝❧❛ss❡s ✭❞❛ ❈❧❛ss❡ ✷ à ❈❧❛ss❡ ✺✮ ♦ ♣ré♠✐♦ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦ é ✐♥❢❡r✐♦r✳ ■st♦ ❞❡✈❡✲s❡ ❛♦ ❢❛❝t♦ ❞❡ ♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ♥ã♦ ❝♦♥s✐❞❡r❛r ❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ s❛í❞❛ ❞♦s s❡❣✉r❛❞♦s ❡✱ ❝♦♠♦ t❛❧✱ ♣r❡✈ê ✉♠❛ ♠❛✐♦r ❛❣❧♦♠❡r❛çã♦ ❞❡ s❡❣✉r❛❞♦s ♥❛s ❝❧❛ss❡s ♠❛✐s ❜❛✐①❛s ❞♦ q✉❡ ❛s ❡st✐♠❛t✐✈❛s ♦❜t✐❞❛s s♦❜ ❛ ♣❡rs♣❡❝t✐✈❛ ❞❡ ✉♠❛ ❝❛rt❡✐r❛ ❛❜❡rt❛✳

      P❛r❛ ❛ ♦❜t❡♥çã♦ ❞❛ ❡s❝❛❧❛ ❞❡ ❝♦♥s✐❞❡r♦✉✲s❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✷✵ ♣♦♥❞❡r❛❞♦r❡s✱ ❞❡✜♥✐❞♦ t❛❧ ❝♦♠♦ ♦ s✐st❡♠❛ ❛❝t✉❛❧✳ ❆♥❛❧✐s❛♥❞♦ ❛ ❡s❝❛❧❛ ❞❡ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ❡s❝❛❧❛ ♦❜t✐❞❛ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ é s✉♣❡r✐♦r à ♦❜t✐❞❛ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ à ❡①❝❡♣çã♦ ❞❛ ❈❧❛ss❡ ✶✳ ❖ ♣ré♠✐♦ ♠é❞✐♦ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❢❡❝❤❛❞♦ ❡ ❛❜❡rt♦ é ✵✱✶✺✶✽✶✺✶✶✶ ❡ ✵✱✶✹✸✸✹✷✻✷✻✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❋✐❣✉r❛ ✸✳✶✺✿ ❊✈♦❧✉çã♦ ❞♦ Pré♠✐♦ ▼é❞✐♦ ✭❊s❝❛❧❛ ❞❡ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦

      ✸✳✸ ❙✐st❡♠❛ ❞❡ ❇♦♥✉s ▼❛❧✉s ❆❧t❡r♥❛t✐✈♦ ♣❛r❛ ❛ ❙❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ✻✸ ❆ ❋✐❣✉r❛ ✐❧✉str❛ ❛ ❡✈♦❧✉çã♦ ❞♦ ♣ré♠✐♦ ♠é❞✐♦ ❞❡ ✉♠ ♥♦✈♦ s❡❣✉r❛❞♦ ❛♦ ❧♦♥❣♦

      ❞❡ ✷✵ ❛♥♦s✱ ✉s❛♥❞♦ ❛ ❡s❝❛❧❛ ❞❡ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❛❜❡rt♦ ❡ ❢❡❝❤❛❞♦✳ ❆♥❛❧✐s❛♥❞♦ ❛ ❋✐❣✉r❛ ✈❡r✐✜❝❛✲s❡ q✉❡✱ ♥♦s ♣r✐♠❡✐r♦s ✻ ❛♥♦s✱ ♦ ♣ré♠✐♦ ♠é❞✐♦ ♥♦

      ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ é s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ✐♥❢❡r✐♦r ❛♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ s❡♥❞♦ q✉❡ ♥♦s r❡st❛♥t❡s ❛♥♦s✱ ♦ ♣ré♠✐♦ ♠é❞✐♦ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦ é ✐♥❢❡r✐♦r ❛♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✳ ❊♥q✉❛♥t♦ q✉❡ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ♦ ♣ré♠✐♦ ✈❛✐ ❛✉♠❡♥t❛♥❞♦ ❛♦ ❧♦♥❣♦ ❞♦s ❛♥♦s ❛té ❛t✐♥❣✐r ❛ ❡st❛❝✐♦♥❛✲ r✐❞❛❞❡✱ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦ ♦ ♣ré♠✐♦ ✈❛✐ ❞✐♠✐♥✉✐♥❞♦ ❛té ❛t✐♥❣✐r ❛ ❡st❛❝✐♦♥❛r✐❞❛❞❡✳ ❊♠ q✉❛❧q✉❡r ✉♠ ❞❡ss❡s ♠♦❞❡❧♦s✱ ♦ ♣ré♠✐♦ ♠é❞✐♦ ♥♦ ✜♥❛❧ ❞♦s ✷✵ ❛♥♦s ❡st❛rá ♣ró①✐♠♦ ❞♦ ♣ré♠✐♦ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✳

      ❆ ❋✐❣✉r❛ ❋✐❣✉r❛ ✸✳✶✻✿ P M ❡♠ ❢✉♥çã♦ ❞❡ λ ✭❊s❝❛❧❛ ❞❡ ❙✳ ❆❧t❡r♥❛t✐✈♦

      ❆ ❚❛❜❡❧❛ ❝♦♠ ♦ ♣ré♠✐♦ ♠é❞✐♦✱ ♦ ❡rr♦ q✉❛❞rát✐❝♦ ♠é❞✐♦ ❡ ❛ ♠❡❞✐❞❛ ❞❡ ❡✜❝✐ê♥❝✐❛✱ ❛ss♦❝✐❛❞♦ ❛ ❝❛❞❛ ✉♠❛ ❞❛s ❡s❝❛❧❛s✳ ❚❛❜❡❧❛ ✸✳✸✸✿ ❊s❝❛❧❛ ❞❡ P▼✱ ❊◗▼ ❡ ▼❡❞✐❞❛ ❞❡ ❊✜❝✐ê♥❝✐❛✿ ❙✳ ❆❧t❡r♥❛t✐✈♦

      ❊s❝❛❧❛ ❞❡ ●✐❧❞❡ ✫ ❙✉♥❞t ❊s❝❛❧❛ ❞❡ ❆♥❞r❛❞❡ ❡ ❙✐❧✈❛ ❈❧❛ss❡ ▼✳ ❋❡❝❤❛❞♦ ▼✳ ❆❜❡rt♦ ▼✳ ❋❡❝❤❛❞♦ ▼✳ ❆❜❡rt♦

      ✶ ✵✱✵✾✵✾✷✺ ✵✱✵✾✾✼✹✽ ✵✱✶✶✸✽✹✼ ✵✱✶✵✻✹✸✼ ✷ ✵✱✷✸✺✸✹✹ ✵✱✶✺✾✺✾✾ ✵✱✶✼✶✼✽✼ ✵✱✶✺✻✶✺✺ ✸ ✵✱✸✼✾✼✻✹ ✵✱✷✶✾✹✹✾ ✵✱✷✺✾✷✶✹ ✵✱✷✷✾✵✾✼ ✹ ✵✱✺✷✹✶✽✸ ✵✱✷✼✾✸✵✵ ✵✱✸✾✶✶✸✻ ✵✱✸✸✻✶✶✶ ✺ ✵✱✻✻✽✻✵✷ ✵✱✸✸✾✶✺✶ ✵✱✺✾✵✶✾✺ ✵✱✹✾✸✶✶✶ ✻ ✵✱✽✶✸✵✷✷ ✵✱✸✾✾✵✵✷ ✵✱✽✾✵✺✻✶ ✵✱✼✷✸✹✹✽

      P M ✵✱✶✹✺✵✺✹ ✵✱✶✹✺✵✺✹ ✵✱✶✺✷✵✸✸ ✵✱✶✹✺✵✾✾ e(∆) ✶✱✵✵✻✸✼✺ ✶✱✵✵✹✽✵✶ ✶✱✶✸✵✼✶✷ ✶✱✵✵✶✹✵✷

      EQM ✵✱✵✷✶✻✺✾ ✵✱✵✹✶✼✾✷ ✵✱✵✷✹✸✸✺ ✵✱✵✹✶✻✺✵

      ✻✹ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❆♥❛❧✐s❛♥❞♦ ❛ ❡s❝❛❧❛ ❧✐♥❡❛r ♦❜t✐❞❛ ♣❡❧♦ ♠♦❞❡❧♦ ❞❡ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ❡s❝❛❧❛ ❞❡ ♣ré♠✐♦s ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ é s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ s✉♣❡r✐♦r ❛♦ ♠♦❞❡❧♦

      ❛❜❡rt♦✱ à ❡①❝❡♣çã♦ ❞❛ ❈❧❛ss❡ ✶✳ ❖ ♣ré♠✐♦ ♠é❞✐♦ ♥♦s ❞♦✐s ♠♦❞❡❧♦s sã♦ ♠✉✐t♦ s❡♠❡✲ ❧❤❛♥t❡s✳ ❆♥❛❧✐s❛♥❞♦ ❛ ♠❡❞✐❞❛ ❞❛ ❡✜❝✐ê♥❝✐❛ ✈❡r✐✜❝❛✲s❡ q✉❡ ❤á ✉♠❛ ♣❡r❞❛ ❞❡ ❡✜❝✐ê♥❝✐❛ ❛♦ ❛❞♦♣t❛r ❛ ❡s❝❛❧❛ ❧✐♥❡❛r ♣❛r❛ ❛♠❜♦s ♦s ♠♦❞❡❧♦s✳

      ❆♥❛❧✐s❛♥❞♦ ❛ ❡s❝❛❧❛ ❣❡♦♠étr✐❝❛ ♦❜t✐❞❛ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ❞❡ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ❡s❝❛❧❛ ❞❡ ♣ré♠✐♦s ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ é s✉♣❡r✐♦r à ❡s❝❛❧❛ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦ ❡♠ t♦❞❛s ❛s ❝❧❛ss❡s✳ ❆♥❛❧✐s❛♥❞♦ ♦ ♣ré♠✐♦ ♠é❞✐♦ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ♥ã♦ ❡st❛❝✐♦♥❛r✲ ✐❞❛❞❡✱ ♦❜t✐❞❛ ❝♦♠ ❡st❛ ❡s❝❛❧❛✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦ ♣ré♠✐♦ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ é s✉♣❡r✐♦r ❛♦ ♠♦❞❡❧♦ ❛❜❡rt♦✳ ❍á ✉♠❛ ♣❡r❞❛ ❞❡ ❡✜❝✐ê♥❝✐❛ ❛♦ ❛❞♦♣t❛r ❛ ❡s❝❛❧❛ ❣❡♦♠étr✐❝❛ ♣❛r❛ ❛♠❜♦s ♦s ♠♦❞❡❧♦s✳

      ❆ ❋✐❣✉r❛ ✐❧✉str❛ ❛ ❡✈♦❧✉çã♦ ❞♦ ♣ré♠✐♦ ♠é❞✐♦ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ♥ã♦ ❡st❛❝✐♦♥❛r✲ ✐❞❛❞❡✱ ❡♠ ❢✉♥çã♦ ❞❡ λ✱ ❝♦♠ ❛ ❡s❝❛❧❛ ❞❡

      ❋✐❣✉r❛ ✸✳✶✼✿ P M ❡♠ ❢✉♥çã♦ ❞❡ λ ✲ ❊s❝❛❧❛ ❞❡ ❙✳ ❆❧t❡r♥❛t✐✈♦

      ✸✳✸✳✼ ▼❡❞✐❞❛s ❞❡ ❆✈❛❧✐❛çã♦

      ❖ ◆í✈❡❧ ▼é❞✐♦ ❘❡❧❛t✐✈♦ ❞❡ ❊st❛❝✐♦♥❛r✐❞❛❞❡ ❚❛❜❡❧❛ ✸✳✸✹✿ ◆í✈❡❧ ▼é❞✐♦ ❘❡❧❛t✐✈♦ ❞❡ ❊st❛❝✐♦♥❛r✐❞❛❞❡✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦

      RSAL ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ▼♦❞❡❧♦ ❆❜❡rt♦

      ❊s❝❛❧❛ ❆❧t❡r♥❛t✐✈❛ ✵✱✵✼✼✽✼✼✺ ✵✱✶✻✶✾✶✻✵ ◆♦r❜❡r❣ ✵✱✵✾✷✻✸✸✶ ✵✱✵✻✶✹✺✷✷

      ❇♦r❣❛♥ ❡t ❛❧ ✵✱✵✽✸✾✾✷✶ ✵✱✵✼✺✹✵✺✹ ●✐❧❞❡ ✫ ❙✉♥❞t ✵✱✵✼✹✾✻✵✻ ✵✱✶✺✶✸✾✺

      ❆✳❙✐❧✈❛ ✵✱✵✹✾✶✻✽✺ ✵✱✵✻✷✻✸✶✷ ❆♥❛❧✐s❛♥❞♦ ❛ ❚❛❜❡❧❛ q✉❡ ❝♦♥té♠ ♦ ♥í✈❡❧ ♠é❞✐♦ r❡❧❛t✐✈♦ ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱

      ✸✳✸ ❙✐st❡♠❛ ❞❡ ❇♦♥✉s ▼❛❧✉s ❆❧t❡r♥❛t✐✈♦ ♣❛r❛ ❛ ❙❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ✻✺ ♠é❞✐♦ r❡❧❛t✐✈♦ ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡ é ♠✉✐t♦ ❜❛✐①♦✱ ♦ q✉❡ ✐♥❞✐❝❛ ❡①✐st✐r ✉♠❛ ❣r❛♥❞❡ ❛❣❧♦♠✲ ❡r❛çã♦ ❞❡ ❛♣ó❧✐❝❡s ♥❛s ❝❧❛ss❡s ♠❛✐s ❜❛✐①❛s ❞♦ s✐st❡♠❛ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✳

      ❆ ❋✐❣✉r❛ ✐❧✉str❛ ❛ ❡✈♦❧✉çã♦ ❞♦ RSAL ❡♠ ❢✉♥çã♦ ❞❡ λ✳ ❆♥❛❧✐s❛♥❞♦✱ ✈❡r✐✜❝❛✲ s❡ q✉❡ ❛ ❡✈♦❧✉çã♦ ❞♦ RSAL ❡♥tr❡ ♦s ❞♦✐s ♠♦❞❡❧♦s é ♠✉✐t♦ ❞✐❢❡r❡♥t❡✳ ◆♦s ❞♦✐s ♠♦✲ ❞❡❧♦s✱ ♦ RSAL ❛✉♠❡♥t❛ ❝♦♠ ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ ♦❜t❡♥❞♦✲s❡✱ ♥♦ ❡♥t❛♥t♦✱ ✈❛❧♦r❡s ❜❛st❛♥t❡ ✐♥❢❡r✐♦r❡s ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ ♣❛r❛ ✈❛❧♦r❡s ♠❛✐s ❡❧❡✈❛❞♦s ❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✳ ■st♦ ❞❡✈❡✲s❡✱ ♥♦✈❛♠❡♥t❡✱ às ❡❧❡✈❛❞❛s t❛①❛s ❞❡ ❛♥✉❧❛çã♦ ♥❛s ❝❧❛ss❡s ♠❛✐s ❡❧❡✈❛❞❛s✳

      ❋✐❣✉r❛ ✸✳✶✽✿ RSAL ❡♠ ❢✉♥çã♦ ❞❡ λ✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦ ❈♦❡✜❝✐❡♥t❡ ❞❡ ❱❛r✐❛çã♦ ◆❛ ❚❛❜❡❧❛ ♣♦❞❡ s❡r ❝♦♥s✉❧t❛❞♦ ♦ ❈♦❡✜❝✐❡♥t❡ ❞❡ ❱❛r✐❛çã♦ ❞♦s ♣ré♠✐♦s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❢❡❝❤❛❞♦ ❡ ❛❜❡rt♦✳

      ❚❛❜❡❧❛ ✸✳✸✺✿ ❈♦❡✜❝✐❡♥t❡ ❞❡ ❱❛r✐❛çã♦✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦ CV

      ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ▼♦❞❡❧♦ ❆❜❡rt♦ ❊s❝❛❧❛ ❆❧t❡r♥❛t✐✈❛ ✵✱✸✷✻✵✽✹ ✵✱✶✻✶✺✵✾

      ◆♦r❜❡r❣ ✶✱✵✾✸✶✸ ✵✱✷✽✸✻✻✹ ❇♦r❣❛♥ ❡t ❛❧ ✶✱✵✵✸✹✸ ✵✱✷✸✵✷✸✷

      ●✐❧❞❡✫❙✉♥❞t ✶✱✵✵✵✶✽ ✵✱✷✵✽✻✵ ❆✳❙✐❧✈❛ ✵✱✽✸✾✼✶✻ ✵✱✷✷✸✷✷✼

      ❆♥❛❧✐s❛♥❞♦ ❛ ❚❛❜❡❧❛ ✈❡r✐✜❝❛✲s❡ q✉❡✱ ♣❛r❛ q✉❛❧q✉❡r ✉♠❛ ❞❛s ❡s❝❛❧❛s✱ ❡①✐st❡ ♠❛✐♦r ✈❛r✐❛❜✐❧✐❞❛❞❡ ❞♦ ♣ré♠✐♦ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✱ ♣❛r❛ ✈❛❧♦r❡s ♠❛✐s ❜❛✐①♦s ❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✳

      ✻✻ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❋✐❣✉r❛ ✸✳✶✾✿ CV ❡♠ ❢✉♥çã♦ ❞❡ λ✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦

      ❆ ❊❧❛st✐❝✐❞❛❞❡ ●❧♦❜❛❧ ❞♦ ❙✐st❡♠❛ ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ❛ ❊❧❛st✐❝✐❞❛❞❡ ●❧♦❜❛❧ ❞♦ s✐st❡♠❛ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❛❜❡rt♦ ❡ ❢❡❝❤❛❞♦✳

      ❚❛❜❡❧❛ ✸✳✸✻✿ ❆ ❊❧❛st✐❝✐❞❛❞❡ ●❧♦❜❛❧✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦ η

      ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ▼♦❞❡❧♦ ❆❜❡rt♦ ❊s❝❛❧❛ ❆❧t❡r♥❛t✐✈❛ ✵✱✶✷✻✶✹✺ ✵✱✵✺✶✶✻✾✻

      ◆♦r❜❡r❣ ✵✱✸✸✸✼✷✻ ✵✱✶✺✾✽✹✺ ❇♦r❣❛♥ ❡t ❛❧ ✵✱✸✷✸✹✾✶ ✵✱✶✶✾✶✺

      ●✐❧❣❡ ❡ ❙✉♥❞t ✵✱✸✶✽✼✵✺ ✵✱✵✼✼✹✽✼✸ ❆✳ ❙✐❧✈❛ ✵✱✷✻✶✻✵✻ ✵✱✶✹✹✶✾✽

      ❆♥❛❧✐s❛♥❞♦ ♦s ✈❛❧♦r❡s ❞❛ ❡❧❛st✐❝✐❞❛❞❡ ❣❧♦❜❛❧ ❞♦ s✐st❡♠❛✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ♣❛r❛ q✉❛❧q✉❡r ✉♠❛ ❞❛s ❡s❝❛❧❛s✱ ❛ ❡❧❛st✐❝✐❞❛❞❡ ❣❧♦❜❛❧ ♦❜t✐❞❛ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ é s✉♣❡r✐♦r à ♦❜t✐❞❛ ♥♦ ♠♦❞❡❧♦ ❛❜❡rt♦✳

      ❋✐❣✉r❛ ✸✳✷✵✿ ❊❧❛st✐❝✐❞❛❞❡ ❞♦ s✐st❡♠❛ ❡♠ ❢✉♥çã♦ ❞❡ λ✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦ ❆♥❛❧✐s❛♥❞♦ ❛ ❋✐❣✉r❛ ✈❡r✐✜❝❛✲s❡ q✉❡✱ ♣❛r❛ ❞❡t❡r♠✐♥❛❞♦s ♥í✈❡✐s ❞❡ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✱ ❛ ❡❧❛st✐❝✐❞❛❞❡ ❞♦ s✐st❡♠❛ ♥♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✱ ♣❛r❛ ❛s ❡s❝❛❧❛s ó♣t✐♠❛s✱

      ✸✳✸ ❙✐st❡♠❛ ❞❡ ❇♦♥✉s ▼❛❧✉s ❆❧t❡r♥❛t✐✈♦ ♣❛r❛ ❛ ❙❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ✻✼ ❡s❝❛❧❛s ♦❜t✐❞❛s✱ ♦❜t❡r✲s❡✲✐❛ q✉❡ ♦ ❛✉♠❡♥t♦ r❡❧❛t✐✈♦ ❞♦ ♣ré♠✐♦ s❡r✐❛ s✉♣❡r✐♦r ❛♦ ❛✉♠❡♥t♦ r❡❧❛t✐✈♦ ❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✳ ❆ ❊❧❛st✐❝✐❞❛❞❡ ❚r❛♥s✐❡♥t❡ ◆❛s ❚❛❜❡❧❛s ♣♦❞❡♠ s❡r ❝♦♥s✉❧t❛❞❛s ❛ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❢❡❝❤❛❞♦ ❡ ❛❜❡rt♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳✳

      ❚❛❜❡❧❛ ✸✳✸✼✿ ❆ ❊❧❛st✐❝✐❞❛❞❡ ❚r❛♥s✐❡♥t❡ ✭▼♦❞❡❧♦ ❋❡❝❤❛❞♦✮✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦ j ❊✳ ❆❧t❡r♥❛t✐✈❛ ◆♦r❜❡r❣ ❇♦r❣❛♥ ❡t ❛❧ ●✐❧❞❡ ❡ ❙✉♥❞t ❆♥❞r❛❞❡ ❡ ❙✐❧✈❛

      ✶ ✵✱✶✶✺✻✽✾ ✵✱✸✶✺✺✶✾ ✵✱✷✹✷✹✸✼✹✵✸ ✵✱✸✵✵✷✶✸✻✻✾ ✵✱✸✵✺✼✵✸✽✾✻ ✷ ✵✱✶✶✻✻✸✻ ✵✱✸✶✵✼✷ ✵✱✷✹✹✹✽✽✷✻✺ ✵✱✷✾✼✸✽✶✻✶✾ ✵✱✸✵✵✽✻✹✶✸✶ ✸ ✵✱✶✶✼✹✹✻ ✵✱✸✵✵✸✹✸ ✵✱✷✹✺✽✽✷✵✶✶ ✵✱✷✽✾✾✷✶✸✾✸ ✵✱✷✾✶✸✻✾✼✻✸ ✹ ✵✱✶✶✼✺✾✼ ✵✱✷✽✺✷✷ ✵✱✷✹✸✽✶✽✼✸ ✵✱✷✼✼✺✽✻✻✺✾ ✵✱✷✼✼✸✻✼✾✾✼ ✺ ✵✱✶✶✻✻✸✸ ✵✱✷✻✻✸✶✹ ✵✱✷✸✺✵✶✽✵✵✷ ✵✱✷✻✵✻✷✼✶✼✹ ✵✱✷✺✾✼✼✽✺✼✺ ✻ ✵✱✶✶✷✶ ✵✱✷✹✹✻✺✻ ✵✱✷✶✻✶✶✷✻✹✻ ✵✱✷✸✾✸✺✶✽✻✶ ✵✱✷✸✾✷✶✼✾✻✸

      ❆♥❛❧✐s❛♥❞♦ ❛ ❚❛❜❡❧❛ ❛♣r❡s❡♥t❛ ✈❛❧♦r❡s s✉♣❡r✐♦r❡s ❡♠ r❡❧❛çã♦ às ♦✉tr❛s ❡s❝❛❧❛s✱ ♣❛r❛ t♦❞❛s ❛s ❝❧❛ss❡s✳

      ❚❛❜❡❧❛ ✸✳✸✽✿ ❆ ❊❧❛st✐❝✐❞❛❞❡ ❚r❛♥s✐❡♥t❡ ✭▼♦❞❡❧♦ ❆❜❡rt♦✮✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦✿ j ❊✳ ❆❧t❡r♥❛t✐✈❛ ◆♦r❜❡r❣ ❇♦r❣❛♥ ❡t ❛❧ ●✐❧❞❡✫ ❙✉♥❞t ❆♥❞r❛❞❡ ❡ ❙✐❧✈❛

      ✶ ✲✵✱✵✹✺✶✵✺✽ ✲✵✱✵✵✷✷✷✺✻ ✲✵✱✵✶✺✶✵✹✻ ✲✵✱✵✷✸✺✺✺✸ ✲✵✱✵✶✻✾✷✶✼ ✷ ✲✵✱✵✵✶✾✸✽✵ ✵✱✵✵✼✼✺✶✵ ✵✱✵✵✺✹✾✽✾ ✵✱✵✵✷✵✻✽✶ ✵✱✵✵✹✺✾✼✽ ✸ ✵✱✵✹✹✽✶✺✼ ✵✱✵✽✼✽✻✼✹ ✵✱✵✽✷✷✺✷✵ ✵✱✵✻✵✸✵✶✶ ✵✱✵✽✺✻✼✼✾ ✹ ✵✱✵✷✻✶✼✺✾ ✵✱✵✺✽✽✽✵✵ ✵✱✵✺✶✾✺✽✶ ✵✱✵✸✻✸✾✵✹ ✵✱✵✻✷✽✶✻✻ ✺ ✵✱✵✵✶✽✸✺✶ ✵✱✵✷✶✸✼✼✽ ✵✱✵✶✵✽✺✽✼ ✵✱✵✵✹✸✾✶✸ ✵✱✵✷✻✽✻✺✻ ✻ ✲✵✱✵✵✶✺✵✹✼ ✵✱✵✵✵✵✼✻✽ ✲✵✱✵✵✶✾✽✸✷ ✲✵✱✵✵✷✵✷✹✸ ✵✱✵✵✵✼✽✺✾

      ❆♥❛❧✐s❛♥❞♦ ❛ ❚❛❜❡❧❛ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ❡s❝❛❧❛ ❛❧t❡r♥❛t✐✈❛ é ❛ q✉❡ ❛♣r❡s❡♥t❛ ✈❛❧♦r❡s ♣❛r❛ ❛ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡ ✐♥❢❡r✐♦r❡s às ♦✉tr❛s ❡s❝❛❧❛s✱ ❡♥q✉❛♥t♦ q✉❡✱ ❞❛ ❈❧❛ss❡ ✶ à ❈❧❛ss❡ ✸✱ ❛ ❡s❝❛❧❛ ❞❡ é ❛ q✉❡ ❛♣r❡s❡♥t❛ ✈❛❧♦r❡s s✉♣❡r✐♦r❡s✱ ❡ ♥❛s r❡st❛♥t❡s ❝❧❛ss❡s ✭❞❛ ❈❧❛ss❡ ✹ à ❈❧❛ss❡ ✻✮ ❛ ❡s❝❛❧❛ ❣❡♦♠étr✐❝❛ é ❛ q✉❡ ❛♣r❡s❡♥t❛ ✈❛❧♦r❡s ♣❛r❛ ❛ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡ s✉♣❡r✐♦r❡s ❡♠ r❡❧❛çã♦ às ♦✉tr❛s ❡s❝❛❧❛s✳ ◆♦t❛✲s❡ q✉❡✱ ❛❧❣✉♠❛s ❝❧❛ss❡s ❛♣r❡s❡♥t❛♠ ❛ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡ ♥❡❣❛t✐✈❛✳ ■st♦ ✐♥❞✐❝✐❛ q✉❡ ✉♠ ❛✉♠❡♥t♦ ♥❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ ♥ã♦ s❡ tr❛❞✉③ ♥✉♠ ❛✉♠❡♥t♦ ❞♦ ✈❛❧♦r ❛❝t✉❛❧ ❞♦s

      ✻✽ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❈♦♠♣❛r❛♥❞♦ ❛s ❡❧❛st✐❝✐❞❛❞❡s ♦❜t✐❞❛s ❡♥tr❡ ♦s ❞♦✐s ♠♦❞❡❧♦s✱ ✈❡r✐✜❝❛✲s❡ ♥♦✈❛♠❡♥t❡ q✉❡ ♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦ ❡st✐♠❛ ✈❛❧♦r❡s s✉♣❡r✐♦r❡s ♣❛r❛ ❛ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡✱ ✉♠❛ ✈❡③ q✉❡ ♥ã♦ t❡♠ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ ❛♥✉❧❛çã♦ ♣♦r ❝❧❛ss❡✱ ♦ q✉❡ ♥❛❧❣✉♠❛s ❝❧❛ss❡s✱ ✈❡r ❚❛❜❡❧❛ sã♦ ❜❛st❛♥t❡s ❡❧❡✈❛❞❛s✳

      ✸✳✸✳✽ ❈♦♠❡♥tár✐♦s às ❊s❝❛❧❛s Ó♣t✐♠❛s

      ❚❛❧ ❝♦♠♦ ♥❛ ❙❡❝çã♦ ♣r❡t❡♥❞❡✲s❡ ❛♥❛❧✐s❛r ❡ ❝♦♠♣❛r❛r ❛s ❡s❝❛❧❛s ó♣t✐♠❛s ❞❡♥tr♦ ❞❡ ❝❛❞❛ ✉♠ ❞♦s ♠♦❞❡❧♦s✳ ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ❆♥❛❧✐s❛♥❞♦ ❛s ❡s❝❛❧❛s ❞❡ ❛♣r❡s❡♥t❛ ♣ré♠✐♦s ✐♥❢❡r✐♦r❡s ❡♠ r❡❧❛çã♦ às ♦✉tr❛s ❡s❝❛❧❛s ❡✱ ♥❛ ❝❧❛ss❡ ♠❛✐s ❛❣r❛✈❛❞❛✱ é ❛ ♠❛✐s ♣❡♥❛❧✐③❛♥t❡✳

      ❊♠ t❡r♠♦s ❞❡ ♠❡❞✐❞❛s ❞❡ ❡✜❝✐ê♥❝✐❛✱ ❛ ❡s❝❛❧❛ ❞❡ r❡✈❡❧❛✲s❡ ❛ ♠❛✐s ❡✜❝✐❡♥t❡✱ ♥♦ ❡♥t❛♥t♦✱ ❛ ❞✐❢❡r❡♥ç❛ ❡♠ r❡❧❛çã♦ às ♦✉tr❛s ❡s❝❛❧❛s ♥ã♦ é s✐❣♥✐✜❝❛t✐✈❛✳ ❍á ✉♠❛ ♣❡r❞❛ ❞❡ ❡✜❝✐ê♥❝✐❛ ❛♦ ❛❞♦♣t❛r ❛ ❡s❝❛❧❛ ❧✐♥❡❛r ♦✉ ❣❡♦♠étr✐❝❛✱ s❡♥❞♦ q✉❡ ❡ss❛ ♣❡r❞❛ é ♠❛✐s s✐❣♥✐✜❝❛t✐✈❛ ♥❛ ❡s❝❛❧❛ ❣❡♦♠étr✐❝❛✳

      ❚❛❜❡❧❛ ✸✳✸✾✿ ❊s❝❛❧❛s Ó♣t✐♠❛s ❡♠ P❡r❝❡♥t❛❣❡♠ ✭▼✳ ❋❡❝❤❛❞♦✮✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦ ❥ ◆♦r❜❡r❣ ❇♦r❣❛♥ ❡t ❛❧ ●✐❧❞❡ ✫ ❙✉♥❞t ❆♥❞r❛❞❡ ❡ ❙✐❧✈❛

      ✶ ✸✸✱✸✽✪ ✸✸✱✸✹✪ ✸✽✱✻✸✪ ✻✻✱✷✼✪ ✷ ✶✵✵✱✵✵✪ ✶✵✵✱✵✵✪ ✶✵✵✱✵✵✪ ✶✵✵✱✵✵✪ ✸ ✶✻✵✱✾✽✪ ✶✺✷✱✻✺✪ ✶✻✶✱✸✼✪ ✶✺✵✱✽✾✪ ✹ ✷✶✻✱✻✸✪ ✷✵✹✱✷✼✪ ✷✷✷✱✼✸✪ ✷✷✼✱✻✾✪ ✺ ✷✻✼✱✹✻✪ ✷✹✾✱✽✺✪ ✷✽✹✱✶✵✪ ✸✹✸✱✺✻✪ ✻ ✸✵✾✱✸✹✪ ✷✾✵✱✸✽✪ ✸✹✺✱✹✻✪ ✺✶✽✱✹✶✪

      ◆♦ q✉❡ s❡ r❡❢❡r❡ às ♠❡❞✐❞❛s ❞❡ ❛✈❛❧✐❛çã♦ ♣r♦♣♦st❛s ♣♦r ❛ ❡s❝❛❧❛ ❞❡ é ❛ q✉❡ ❛♣r❡s❡♥t❛ ✉♠ RSAL ❡ CV ♠❛✐s ❡❧❡✈❛❞♦✳ ❆ ❡s❝❛❧❛ ❞❡ tr❛❞✉③✐r✲s❡✲á ♦ s✐st❡♠❛ ♠❛✐s ❡❧ást✐❝♦✳ ▼♦❞❡❧♦ ❆❜❡rt♦ ❆♥❛❧✐s❛♥❞♦ ❛s ❡s❝❛❧❛s ó♣t✐♠❛s ♦❜t✐❞❛s ✉s❛♥❞♦ ♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦ ♣ré♠✐♦ ♠é❞✐♦ ♥❛ ❡s❝❛❧❛ ❞❡ é ❧✐❣❡✐r❛♠❡♥t❡ s✉♣❡r✐♦r às ♦✉tr❛s ❡s❝❛❧❛s ❡ ♦s ♣ré♠✐♦s

      ✸✳✹ ❈♦♠♣❛r❛çã♦ ❞♦s ❉♦✐s ❙✐st❡♠❛s ❞❡ ❇♦♥✉s ▼❛❧✉s ✻✾ ❘❡❧❛t✐✈❛♠❡♥t❡ ❛♦ EQM✱ ✈❡r✐✜❝❛✲s❡ q✉❡ t♦❞❛s ❛s ❡s❝❛❧❛s ❛♣r❡s❡♥t❛♠ ✉♠ EQM s❡♠❡❧❤❛♥t❡✳ ❆ ❡✜❝✐ê♥❝✐❛ ♥❛s ❡s❝❛❧❛s ❞❡ ❛♣r❡✲ s❡♥t❛♠ ✉♠ ✈❛❧♦r s❡♠❡❧❤❛♥t❡✳ ❍á ✉♠❛ ♣❡r❞❛ ❞❡ ❡✜❝✐ê♥❝✐❛ ❛♦ ❛❞♦♣t❛r ❛ ❡s❝❛❧❛ ❧✐♥❡❛r ♦✉ ❣❡♦♠étr✐❝❛✱ ♥♦ ❡♥t❛♥t♦ ❡ss❛ ♣❡r❞❛ ♥ã♦ é s✐❣♥✐✜❝❛t✐✈❛✱ ❡ s❡rá ♣r❡❢❡rí✈❡❧ ❛ ✉t✐❧✐③❛r ✉♠❛ ❡s❝❛❧❛ ❝✉❥♦s ❛❣r❛✈❛♠❡♥t♦s ♥ã♦ ❡✈♦❧✉❡♠ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ r✐s❝♦ q✉❡ ♦ s❡❣✉r❛❞♦ r❡♣r❡s❡♥t❛ ♣❛r❛ ❛ s❡❣✉r❛❞♦r❛✳

      ❊♠ r❡❧❛çã♦ às ♠❡❞✐❞❛ ❞❡ ❛✈❛❧✐❛çã♦✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ❡s❝❛❧❛ ❧✐♥❡❛r é ❛ q✉❡ ❛♣r❡s❡♥t❛ ✉♠ RSAL s✉♣❡r✐♦r ❡♠ r❡❧❛çã♦ às ♦✉tr❛s ❡s❝❛❧❛s✱ ❡♥q✉❛♥t♦ q✉❡ ❛ ❡s❝❛❧❛ ❞❡ é ❛ q✉❡ ❛♣r❡s❡♥t❛ ✉♠ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✈❛r✐❛çã♦ s✉♣❡r✐♦r ❡ é ❛ ❡s❝❛❧❛ q✉❡ t♦r♥❛ ♦ s✐st❡♠❛ ♠❛✐s ❡❧ást✐❝♦✳

      ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ❛s ❡s❝❛❧❛s ó♣t✐♠❛s ❞❡ ♣ré♠✐♦s ❡♠ ♣❡r❝❡♥t❛❣❡♠ ❞♦ ♣ré♠✐♦ ❞❡ ❡♥tr❛❞❛✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦ ♠♦♥t❛♥t❡ ❛ss♦❝✐❛❞♦ ❛ ❝❛❞❛ s✐♥✐str♦ ✉♥✐tár✐♦✳ ❚❛❜❡❧❛ ✸✳✹✵✿ ❊s❝❛❧❛s Ó♣t✐♠❛s ❡♠ P❡r❝❡♥t❛❣❡♠ ✭▼♦❞❡❧♦ ❆❜❡rt♦✮✿ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦

      ❥ ◆♦r❜❡r❣ ❇♦r❣❛♥ ❡t ❛❧ ●✐❧❞❡ ✫ ❙✉♥❞t ❆♥❞r❛❞❡ ❡ ❙✐❧✈❛ ✶ ✻✺✱✶✻✪ ✼✶✱✶✵✪ ✻✷✱✾✽✪ ✻✽✱✸✺✪ ✷ ✶✵✵✪ ✶✵✵✪ ✶✵✵✪ ✶✵✵✪ ✸ ✶✽✶✱✻✸✪ ✶✼✻✱✸✽✪ ✶✸✼✱✵✷✪ ✶✹✻✱✸✶✪ ✹ ✷✻✸✱✵✽✪ ✷✺✻✱✶✽✪ ✶✼✹✱✵✹✪ ✷✶✹✱✵✺✪ ✺ ✸✻✷✱✻✵✪ ✸✻✷✱✾✺✪ ✷✶✶✱✵✻✪ ✸✶✸✱✶✼✪ ✻ ✸✺✻✱✶✽✪ ✸✹✶✱✻✻✪ ✷✹✽✱✵✼✪ ✹✺✽✱✶✾✪

      ❆♥❛❧✐s❛♥❞♦ ❛ ❚❛❜❡❧❛ ✈❡r✐✜❝❛✲s❡ q✉❡ ♣❛r❛ q✉❛❧q✉❡r ✉♠❛ ❞❛s ❡s❝❛❧❛s✱ ♦ ♣ré♠✐♦ ❛ ❛♣❧✐❝❛r à ❈❧❛ss❡ ✶ ♥ã♦ ❞✐❢❡r❡ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ❡♥tr❡ ❡❧❛s✳ ❆ ❡s❝❛❧❛ ❞❡ é ❛ ❡s❝❛❧❛ ♠❛✐s ❛❝♦♥s❡❧❤á✈❡❧ ❡♠ ❝♦♠♣❛r❛çã♦ ❝♦♠ ❛s r❡st❛♥t❡s ❡s❝❛❧❛s✱ ♣♦rq✉❡ ♥❛s ❡s❝❛❧❛s ❞❡ ♦ ♣ré♠✐♦ ❛ ❛♣❧✐❝❛r ♥ã♦ ❛✉♠❡♥t❛ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡✱ ❡ ❛ ❡s❝❛❧❛ ❞❡ ❛♣r❡s❡♥t❛ ♣ré♠✐♦s ❜❛st❛♥t❡ ❡❧❡✈❛❞♦s✱ ♦ q✉❡ s✉❣❡r❡ s❡r ♣♦✉❝♦ ✈✐á✈❡❧ ❞♦ ♣♦♥t♦ ❞❡ ✉♠ ♣♦st♦ ❞❡ ✈✐st❛ ❝♦♠❡r❝✐❛❧✳

      

    ✸✳✹ ❈♦♠♣❛r❛çã♦ ❞♦s ❉♦✐s ❙✐st❡♠❛s ❞❡ ❇♦♥✉s ▼❛❧✉s

      ◆❡st❛ s❡❝çã♦ s❡rã♦ ❢❡✐t❛s ❛♥á❧✐s❡s ❝♦♠♣❛r❛t✐✈❛s ❡♥tr❡ ♦s ❞♦✐s s✐st❡♠❛s ❡st✉❞❛❞♦s ❛♥t❡✲ r✐♦r♠❡♥t❡✳ P❛r❛ t❛❧✱ s❡rã♦ ✉t✐❧✐③❛❞❛s ❛s ♠❡❞✐❞❛s ❞❡ ❛✈❛❧✐❛çã♦ ♣r♦♣♦st❛s ♣♦r ❈♦♠ ❜❛s❡ ♥♦s r❡s✉❧t❛❞♦s ❥á ♦❜t✐❞♦s s❡rã♦ ❛♣r❡s❡♥t❛❞❛s ❛s r❡s♣❡❝t✐✈❛s ❝♦♥✲ ❝❧✉sõ❡s✳

      ✼✵ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛

      ✸✳✹✳✶ ❙♦❜ ❛ P❡rs♣❡❝t✐✈❛ ❞❛ ❈❛rt❡✐r❛ ❋❡❝❤❛❞❛

      ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ♦s ♣ré♠✐♦s ♠é❞✐♦s ♣❛r❛ ❝❛❞❛ ✉♠❛ ❞❛s ❡s❝❛❧❛s r❡❢❡r❡♥❝✐❛❞❛s ♥❛s s❡❝çõ❡s ❛♥t❡r✐♦r❡s✳ ◆♦t❛♠♦s q✉❡ ❛ ❡s❝❛❧❛ ❆❝t✉❛❧✴❆❧t❡r♥❛t✐✈❛ s❡ r❡❢❡r❡ ❛♦s ❞❡s❝♦♥t♦s✴❛❣r❛✈❛♠❡♥t♦s ❛

      ❛♣❧✐❝❛r ❛♦ ♣ré♠✐♦ ❛ ♣r✐♦r✐ ✉t✐❧✐③❛❞❛ ♣❡❧❛ ❙❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ r❡♣r❡s❡♥t❛♥❞♦✱ ♣♦rt❛♥t♦✱ ❛ ♣❡r❝❡♥t❛❣❡♠ ❞♦ ♣ré♠✐♦ ❛ ♣r✐♦r✐ q✉❡ ♦ s❡❣✉r❛❞♦ ❞❡✈❡rá ♣❛❣❛r✱ ❡♥q✉❛♥t♦ q✉❡ ❛s ❡s❝❛❧❛s ó♣t✐♠❛s ♣r♦♣♦st❛s ♣❡❧♦s ❞✐✈❡rs♦s ❛✉t♦r❡s✱ s❡ r❡❢❡r❡♠ ❛♦ ✈❛❧♦r ❡st✐♠❛❞♦ ♣❛r❛ ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ s✐♥✐str❛❧✐❞❛❞❡ ❞❡ ❝❛❞❛ ❝❧❛ss❡✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦ ❝✉st♦ ♠é❞✐♦ ❞❡ ✉♠ s✐♥✐str♦ ❝♦♠♦ ❛ ✉♥✐❞❛❞❡ ♠♦♥❡tár✐❛✳ ❆ss✐♠✱ ❡♠ t❡r♠♦s ❞❡ Pré♠✐♦ ▼é❞✐♦✱ ❛s ❡s❝❛❧❛s ❛❝t✉❛❧ ❡ ó♣t✐♠❛s ♥ã♦ sã♦ ❞✐r❡❝t❛♠❡♥t❡ ❝♦♠♣❛rá✈❡✐s✳

      ❚❛❜❡❧❛ ✸✳✹✶✿ ❘❡s✉♠♦ ❞♦ P M✿ ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ Pré♠✐♦ ▼é❞✐♦

      ❊s❝❛❧❛s ❙✐st❡♠❛ ❆❝t✉❛❧ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦ ❆❝t✉❛❧ ✴ ❆❧t❡r♥❛t✐✈❛ ✼✾✱✼✸✼✸✶✵✷✽ ✽✵✱✶✷✹✶

      ◆♦r❜❡r❣ ✵✱✶✹✺✵✺✸✻✺✶ ✵✱✶✹✺✵✺✹ ❇♦r❣❛♥ ❡t ❛❧❧ ✵✱✶✹✺✵✺✸✻✺✶ ✵✱✶✹✺✵✺✸✻✺✶

      ●✐❧❞❡ ❡ ❙✉♥❞t ✵✱✶✹✺✵✺✸✻✺✶ ✵✱✶✹✺✵✺✸✻✺✶ ❆✳ ❙✐❧✈❛ ✵✱✶✹✺✶✾✷✽✶ ✵✱✶✺✷✵✸✸✹✽✻

      ❖ ♣ré♠✐♦ ♠é❞✐♦ é ❜❛st❛♥t❡ s❡♠❡❧❤❛♥t❡ ♣❛r❛ ♦s ❞♦✐s s✐st❡♠❛s ❛♥❛❧✐s❛❞♦s✱ s❡♥❞♦ q✉❡ ♥♦ s✐st❡♠❛ ❛❧t❡r♥❛t✐✈♦ é ❧✐❣❡✐r❛♠❡♥t❡ s✉♣❡r✐♦r✱ ♣❛r❛ t♦❞❛s ❛s ❡s❝❛❧❛s ❡st✉❞❛❞❛s✳ ◆♦

      ♦

      s✐st❡♠❛ ❛❝t✉❛❧✱ ♦ ♣ré♠✐♦ ♠é❞✐♦ ❡st❛❜✐❧✐③❛ ♥♦ ✷ ❛♥♦✱ ♦ ♠❡s♠♦ ♥ã♦ ❛❝♦♥t❡❝❡ ❝♦♠ ♦

      ♦

      s✐st❡♠❛ ❛❧t❡r♥❛t✐✈♦✱ ❡st❛❜✐❧✐③❛♥❞♦ ♥♦ ✶✺ ❛♥♦✳ ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ✉♠ r❡s✉♠♦ ❞♦ RSAL ♦❜t✐❞♦ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✱ ♣❛r❛

      ♦s ❞♦✐s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s ❡st✉❞❛❞♦s✱ ❞❡t❡r♠✐♥❛❞♦ ♥❛s s❡❝çõ❡s ❛♥t❡r✐♦r❡s✳ ❚❛❜❡❧❛ ✸✳✹✷✿ ❘❡s✉♠♦ ❞♦ RSAL✿ ▼♦❞❡❧♦ ❋❡❝❤❛❞♦

      ❘❙❆▲ ❊s❝❛❧❛s ❙✐st❡♠❛ ❆❝t✉❛❧ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦

      ❆❝t✉❛❧ ✴ ❆❧t❡r♥❛t✐✈❛ ✵✱✵✼✹✾✵✷✹ ✵✱✵✼✼✽✼✼✺ ◆♦r❜❡r❣ ✵✱✵✼✾✸✶✷✾ ✵✱✵✾✷✻✸✸✶

      ❇♦r❣❛♥ ❡t ❛❧ ✵✱✵✽✵✸✼✶✷ ✵✱✵✾✸✾✺✷✻ ●✐❧❞❡ ✫ ❙✉♥❞t ✵✱✵✽✽✽✾✺✾ ✵✱✵✽✺✵✺✵

      ❆✳ ❙✐❧✈❛ ✵✱✵✸✺✷✾✵✺ ✵✱✵✺✾✸✽✷✸ ❈♦♠♣❛r❛♥❞♦ ♦s RSAL ♦❜t✐❞♦s ♥♦s ❞♦✐s s✐st❡♠❛s✱ ❡st❛ ♠❡❞✐❞❛ ✐♥❞✐❝❛ q✉❡ ✉s❛♥❞♦

      ❛s ❡s❝❛❧❛s ó♣t✐♠❛s✱ à ❡①❝❡♣çã♦ ❞❛ ❡s❝❛❧❛ ❞❡ ❛s ❛♣ó❧✐❝❡s ❡♥❝♦♥✲

      ✸✳✹ ❈♦♠♣❛r❛çã♦ ❞♦s ❉♦✐s ❙✐st❡♠❛s ❞❡ ❇♦♥✉s ▼❛❧✉s ✼✶ ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ✉♠ r❡s✉♠♦ ❞♦ CV ♦❜t✐❞♦ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ❢❡❝❤❛❞♦✱ ♣❛r❛

      ♦s ❞♦✐s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s ❡st✉❞❛❞♦s✱ ❞❡t❡r♠✐♥❛❞♦ ♥❛s s❡❝çõ❡s ❛♥t❡r✐♦r❡s✳ ❚❛❜❡❧❛ ✸✳✹✸✿ ❘❡s✉♠♦ ❞♦ CV ✿ ▼♦❞❡❧♦ ❋❡❝❤❛❞♦

      ❈♦❡✜❝✐❡♥t❡ ❞❡ ❱❛r✐❛çã♦ ❊s❝❛❧❛s ❙✐st❡♠❛ ❆❝t✉❛❧ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦

      ❆❝t✉❛❧✴ ❆❧t❡r♥❛t✐✈❛ ✵✱✷✹✼✽✶✷ ✵✱✸✷✻✵✽✹ ◆♦r❜❡r❣ ✵✱✽✷✹✵✹✾ ✶✱✵✾✸✶✸✵

      ❇♦r❣❛♥ ❡t ❛❧ ✵✱✼✽✼✾✽✼ ✶✱✵✵✵✸✹✸ ●✐❧❞❡ ✫ ❙✉♥❞t ✵✱✼✶✽✽✺✷ ✶✱✵✵✵✶✽✵

      ❆✳ ❙✐❧✈❛ ✵✱✻✼✹✻✽✶ ✵✱✽✸✾✼✶✻ ❈♦♠♣❛r❛♥❞♦ ♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ ✈❛r✐❛çã♦ ♦❜t✐❞♦s ♣❛r❛ ♦s ❞♦✐s s✐st❡♠❛s✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦ s✐st❡♠❛ ❛❧t❡r♥❛t✐✈♦ ❛♣r❡s❡♥t❛ ✉♠ CV s✉♣❡r✐♦r ❛♦ s✐st❡♠❛ ❛❝t✉❛❧✱ ♦✉ s❡❥❛✱ ❡①✐st❡

      ♠❛✐♦r ✈❛r✐❛❜✐❧✐❞❛❞❡ ❞♦ ♣ré♠✐♦ ♥♦ s✐st❡♠❛ ❛❧t❡r♥❛t✐✈♦✳ ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ✉♠ r❡s✉♠♦ ❞❛ ❊❧❛st✐❝✐❞❛❞❡ ●❧♦❜❛❧ ♦❜t✐❞♦ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦

      ❢❡❝❤❛❞♦✱ ♣❛r❛ ♦s ❞♦✐s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s ❡st✉❞❛❞♦s✱ ❞❡t❡r♠✐♥❛❞♦ ♥❛s s❡❝çõ❡s ❛♥t❡r✐♦r❡s✳

      ❚❛❜❡❧❛ ✸✳✹✹✿ ❘❡s✉♠♦ ❞❛ ❊❧❛st✐❝✐❞❛❞❡ ●❧♦❜❛❧✿ ▼♦❞❡❧♦ ❋❡❝❤❛❞♦ ❊❧❛st✐❝✐❞❛❞❡ ●❧♦❜❛❧

      ❊s❝❛❧❛s ❙✐st❡♠❛ ❆❝t✉❛❧ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦ ❆❝t✉❛❧ ✴ ❆❧t❡r♥❛t✐✈❛ ✵✱✵✽✹✶✺✹ ✵✱✶✷✻✶✹✺

      ◆♦r❜❡r❣ ✵✱✷✹✼✷✻✽ ✵✱✸✸✸✼✷✻ ❇♦r❣❛♥ ❡t ❛❧ ✵✱✷✹✾✸✺✽ ✵✱✸✷✸✹✾✶

      ●✐❧❞❡ ✫ ❙✉♥❞t ✵✱✷✻✽✸✹✻ ✵✱✸✶✽✼✵✺ ❆✳ ❙✐❧✈❛ ✵✱✷✷✺✵✵✺ ✵✱✷✻✶✻✵✻

      ❆♥❛❧✐s❛♥❞♦ ❛ ❚❛❜❡❧❛ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦ s✐st❡♠❛ ❛❧t❡r♥❛t✐✈♦ é ♠❛✐s ❡❧ást✐❝♦ q✉❡ ♦ s✐st❡♠❛ ❛❝t✉❛❧✱ ♣♦rt❛♥t♦✱ r❡s♣♦♥❞❡rá ♠❡❧❤♦r ❛ ❛❧t❡r❛çõ❡s ❞❡ s✐♥✐str❛❧✐❞❛❞❡✳ ❊st❛ ❡r❛ ✉♠❛ s✐t✉❛çã♦ ❡①♣❡❝tá✈❡❧ ✉♠❛ ✈❡③ q✉❡ ❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦ ❛❝t✉❛✐s ♣❡r♠✐t❡♠ q✉❡ ♦ ❛✉♠❡♥t♦ ❞❛ s✐♥✐str❛❧✐❞❛❞❡ s❡ tr❛❞✉③❛ ♥✉♠❛ ❞✐♠✐♥✉✐çã♦ ❞♦ ♣ré♠✐♦✳ ❖ ❢❛❝t♦ ❞❡ s❡ ❝♦rr✐❣✐r ❡st❛ s✐t✉❛çã♦ tr❛❞✉③✐r✲s❡✲á✱ ♥❛t✉r❛❧♠❡♥t❡✱ ♥✉♠ s✐st❡♠❛ ♠❛✐s ❡❧ást✐❝♦✳

      ✸✳✹✳✷ ❙♦❜ ❛ P❡rs♣❡❝t✐✈❛ ❞❛ ❈❛rt❡✐r❛ ❆❜❡rt❛

      ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ✉♠ r❡s✉♠♦ ❞♦ P M ♦❜t✐❞♦ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ ♣❛r❛ ♦s ❞♦✐s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s ❡st✉❞❛❞♦s✱ ❞❡t❡r♠✐♥❛❞♦ ♥❛s s❡❝çõ❡s ❛♥t❡r✐♦r❡s✳

      ❆♥❛❧✐s❛♥❞♦ ❛s ❡s❝❛❧❛s ó♣t✐♠❛s ❞❡ ♣ré♠✐♦s ♦❜t✐❞❛s ♥♦s ❞♦✐s s✐st❡♠❛s✱ ✈❡r✐✜❝❛✲s❡

      ✼✷ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ❚❛❜❡❧❛ ✸✳✹✺✿ ❘❡s✉♠♦ ❞♦ P M✿ ▼♦❞❡❧♦ ❆❜❡rt♦

      Pré♠✐♦ ▼é❞✐♦ ❊s❝❛❧❛s ❙✐st❡♠❛ ❆❝t✉❛❧ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦

      ❆❝t✉❛❧ ✴ ❆❧t❡r♥❛t✐✈❛ ✾✷✱✵✷✵✻✹✶ ✾✶✱✵✹✾✶✵✵ ◆♦r❜❡r❣ ✵✱✶✹✺✵✻✹ ✵✱✶✹✺✶✺✼

      ❇♦r❣❛♥ ❡t ❛❧ ✵✱✶✹✺✵✺✹ ✵✱✶✹✺✵✺✹ ●✐❧❞❡ ❡ ❙✉♥❞t ✵✱✶✹✶✼✶✼ ✵✱✶✹✺✵✺✹

      ❆✳ ❙✐❧✈❛ ✵✱✶✹✺✶✾✸ ✵✱✶✹✺✵✾✾ ❡♥q✉❛♥t♦ q✉❡✱ ♥❛s ❝❧❛ss❡s ❛❣r❛✈❛❞❛s ❞♦ s✐st❡♠❛✱ ♦ s✐st❡♠❛ ❛❝t✉❛❧ é ♠❛✐s s❡✈❡r♦✳ ◆♦ ❡♥t❛♥t♦✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦s ♣ré♠✐♦s ♠é❞✐♦s ♦❜t✐❞♦s ♥♦s ❞♦✐s s✐st❡♠❛s sã♦ ❜❛st❛♥t❡s s❡♠❡❧❤❛♥t❡s✳

      ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ✉♠ r❡s✉♠♦ ❞♦ RSAL ♦❜t✐❞♦ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ ♣❛r❛ ♦s ❞♦✐s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s ❡st✉❞❛❞♦s✱ ♦❜t✐❞❛s ♥❛s s❡❝çõ❡s ❛♥t❡r✐♦r❡s✳

      ❚❛❜❡❧❛ ✸✳✹✻✿ ❘❡s✉♠♦ ❞♦ RSAL✿ ▼♦❞❡❧♦ ❆❜❡rt♦ ❘❙❆▲

      ❊s❝❛❧❛s ❙✐st❡♠❛ ❆❝t✉❛❧ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦ ❆❝t✉❛❧ ✴ ❆❧t❡r♥❛t✐✈♦ ✵✱✶✻✾✸✾✵ ✵✱✶✻✶✾✶✻

      ◆♦r❜❡r❣ ✵✱✵✽✻✻✽✹ ✵✱✵✻✶✹✺✷ ❇♦r❣❛♥ ❡t ❛❧ ✵✱✼✼✽✻✵✹ ✵✱✼✺✹✵✺✹

      ●✐❧❞❡ ✫ ❙✉♥❞t ✵✱✶✻✷✸✺✺ ✵✱✶✺✶✸✾✺ ❆✳ ❙✐❧✈❛ ✵✱✵✺✼✹✼✾ ✵✱✵✻✷✻✸✶

      ❆♥❛❧✐s❛♥❞♦ ♦s RSAL ❞♦s ❞♦✐s s✐st❡♠❛s✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ✉s❛♥❞♦ ❛s ❡s❝❛❧❛s ❛❝t✉❛❧ ❡ ❛❧t❡r♥❛t✐✈❛✱ ♦ RSAL ❞♦s ❞♦✐s ♠♦❞❡❧♦s é s❡♠❡❧❤❛♥t❡✱ ✐st♦ ❥✉st✐✜❝❛✲s❡ ♣❡❧♦ ❢❛❝t♦ ❞❡✱ ♦s ❞❡s❝♦♥t♦s ❡ ❛❣r❛✈❛♠❡♥t♦s ❛♣❧✐❝❛❞♦s ♥♦s ❞♦✐s ♠♦❞❡❧♦s s❡r ♦ ♠❡s♠♦✱ ♦ q✉❡ ♦s ❞✐❢❡r❡♥✲ ❝✐❛ sã♦ ❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦✳ ❯s❛♥❞♦ ❛s ♦✉tr❛s ❡s❝❛❧❛s✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦ RSAL ♥♦ s✐st❡♠❛ ❛❝t✉❛❧ é s✉♣❡r✐♦r ♥♦ s✐st❡♠❛ ❛❧t❡r♥❛t✐✈♦✱ ❡①❝❡♣t♦ q✉❛♥❞♦ s❡ ❝♦♥s✐❞❡r❛ ❛ ❡s❝❛❧❛ ❞❡ ♦ q✉❡ s❡ ❥✉st✐✜❝❛ ♣❡❧♦ ❢❛❝t♦ ❞❡ ♥♦ s✐st❡♠❛ ❛❝t✉❛❧ ❛s ❡s❝❛❧❛s ó♣t✐♠❛s ❛♣r❡s❡♥t❛r❡♠ ✉♠ ♣ré♠✐♦ s✉♣❡r✐♦r ♥❛ ❝❧❛ss❡ ♠❛✐s ❛❣r❛✈❛❞❛✳

      ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ✉♠ r❡s✉♠♦ ❞♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✈❛r✐❛çã♦ ♦❜t✐❞♦ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ ♣❛r❛ ♦s ❞♦✐s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s ❡st✉❞❛❞♦s✱ ♦❜t✐❞❛s ♥❛s s❡❝çõ❡s ❛♥t❡r✐♦r❡s✳

      ❆♥❛❧✐s❛♥❞♦ ♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✈❛r✐❛çã♦ ❞♦s ♣ré♠✐♦s ♦❜t✐❞♦ ♥♦s ❞♦✐s s✐st❡♠❛s✱ ✈❡r✐✜❝❛✲ s❡ q✉❡ ♣❛r❛ ❛ ❡s❝❛❧❛ ❛❝t✉❛❧ ❡ ❛ ❡s❝❛❧❛ ❛❧t❡r♥❛t✐✈❛✱ ❛ ✈❛r✐❛çã♦ ❞♦s ♣ré♠✐♦s é ❜❛st❛♥t❡ s❡♠❡❧❤❛♥t❡✱ ❡♥q✉❛♥t♦ q✉❡ ♣❛r❛ ❛s ❡s❝❛❧❛s ó♣t✐♠❛s✱ ♦ ♣ré♠✐♦ ♠é❞✐♦ ♥♦ s✐st❡♠❛ ❛❝t✉❛❧

      ✸✳✹ ❈♦♠♣❛r❛çã♦ ❞♦s ❉♦✐s ❙✐st❡♠❛s ❞❡ ❇♦♥✉s ▼❛❧✉s ✼✸ ❚❛❜❡❧❛ ✸✳✹✼✿ ❘❡s✉♠♦ ❞♦ CV ✿ ▼♦❞❡❧♦ ❆❜❡rt♦

      ❈♦❡✜❝✐❡♥t❡ ❞❡ ❱❛r✐❛çã♦ ❊s❝❛❧❛s ❙✐st❡♠❛ ❆❝t✉❛❧ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦

      ❆❝t✉❛❧ ❆❧t❡r♥❛t✐✈♦ ✵✱✶✻✺✷✹✻ ✵✱✶✻✶✺✵✾ ◆♦r❜❡r❣ ✵✱✸✻✵✶✽✶ ✵✱✷✽✸✻✻✹

      ❇♦r❣❛♥ ❡t ❛❧ ✵✱✸✵✹✻✻✵ ✵✱✷✸✵✷✸✷ ●✐❧❞❡ ✫ ❙✉♥❞t ✵✱✷✻✹✵✷✸ ✵✱✷✵✽✻✵✵

      ❆✳ ❙✐❧✈❛ ✵✱✷✽✷✻✽✸ ✵✱✷✷✸✷✷✼ ❆ ❚❛❜❡❧❛ ❝♦♥té♠ ✉♠ r❡s✉♠♦ ❞❛ ❡❧❛st✐❝✐❞❛❞❡ ❣❧♦❜❛❧ ❞♦s s✐st❡♠❛s ♦❜t✐❞♦ ❛tr❛✈és

      ❞♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ ❞❡t❡r♠✐♥❛❞♦ ♥❛s s❡❝çõ❡s ❛♥t❡r✐♦r❡s✳ ❚❛❜❡❧❛ ✸✳✹✽✿ ❘❡s✉♠♦ ❞❛ ❊❧❛st✐❝✐❞❛❞❡ ●❧♦❜❛❧✿ ▼♦❞❡❧♦ ❆❜❡rt♦

      ❊❧❛st✐❝✐❞❛❞❡ ❞♦ ❙✐st❡♠❛ ❊s❝❛❧❛s ❙✐st❡♠❛ ❆❝t✉❛❧ ❙✐st❡♠❛ ❆❧t❡r♥❛t✐✈♦

      ❆❝t✉❛❧ ❆❧t❡r♥❛t✐✈♦ ✵✱✵✹✸✹✻✾ ✵✱✵✺✶✶✼✵ ◆♦r❜❡r❣ ✵✱✶✵✻✸✼✷ ✵✱✶✺✾✽✹✺

      ❇♦r❣❛♥ ❡t ❛❧ ✵✱✵✾✵✽✻✺ ✵✱✶✶✾✶✺✵ ●✐❧❞❡ ✫ ❙✉♥❞t ✵✱✵✽✶✾✶✶ ✵✱✵✼✼✹✽✼

      ❆✳ ❙✐❧✈❛ ✵✱✶✺✵✷✹✹ ✵✱✶✹✹✶✾✽ ❆♥❛❧✐s❛♥❞♦ ❛s ❡❧❛st✐❝✐❞❛❞❡s ❞♦s s✐st❡♠❛s✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦ s✐st❡♠❛ ❛❧t❡r♥❛t✐✈♦ é ♠❛✐s

      ❡❧ást✐❝♦✱ ❡①❝❡♣t♦ q✉❛♥❞♦ s❡ ❝♦♥s✐❞❡r❛♠ ❛s ❡s❝❛❧❛s ❞❡ ❊st❛ ❡r❛ ✉♠❛ s✐t✉❛çã♦ ❡①♣❡❝tá✈❡❧✱ ❞❛❞♦ q✉❡ ♥♦ s✐st❡♠❛ ❛❝t✉❛❧ ♦ ❛✉♠❡♥t♦ ❞❛ s✐♥✐str❛❧✐❞❛❞❡ tr❛❞✉③✲s❡ ♥✉♠❛ ❞✐♠✐♥✉✐çã♦ ❞♦ ♣ré♠✐♦✳

      ❘❡❧❛t✐✈❛♠❡♥t❡ ❛♦s ❞♦✐s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s ❡st✉❞❛❞♦s✱ ♦ q✉❡ ♦s ❞✐❢❡r❡♥❝✐❛ sã♦ ❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦ ❡♥tr❡ ❛s ❝❧❛ss❡s ❞❡ ❜♦♥✉s✳ ❈♦♠♦ ❥á ❢♦✐ r❡❢❡r✐❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❛s ❛❝t✉❛✐s r❡❣r❛s ❛♣r❡s❡♥t❛♠ ✐♥❝♦❡rê♥❝✐❛s✱ ❡ ♥❡st❡ s❡♥t✐❞♦✱ ♦ s✐st❡♠❛ ❛❧t❡r♥❛t✐✈♦ r❡✲ s♦❧✈❡ ❛❧❣✉♥s ❞♦s ♣r♦❜❧❡♠❛s ❞♦ ❛❝t✉❛❧ s✐st❡♠❛✱ ❞❛❞♦ q✉❡ é ✉♠ s✐st❡♠❛ ♠❛✐s ❡✜❝✐❡♥t❡ ❡ ❡q✉✐❧✐❜r❛❞♦✳

      ❈♦♥❝❧✉sã♦

      ❖ ♦❜❥❡❝t✐✈♦ ❞♦ ♣r❡s❡♥t❡ ❡st✉❞♦ ❢♦✐ ❛✈❛❧✐❛r ♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ✭SBM✮ ❞❛ s❡❣✉✲ r❛❞♦r❛ ❝❛❜♦✲✈❡r❞✐❛♥❛ ●❛r❛♥t✐❛✱ ❈♦♠♣❛♥❤✐❛ ❞❡ ❙❡❣✉r♦s ❞❡ ❈❛❜♦ ❱❡r❞❡ ❙✳❆✳✱ q✉❡r s♦❜ ❛ ♣❡rs♣❡❝t✐✈❛ ❞❡ ✉♠❛ ❝❛rt❡✐r❛ ❢❡❝❤❛❞❛✱ ✉t✐❧✐③❛♥❞♦ ❛ ♠❡t♦❞♦❧♦❣✐❛ ❝❧áss✐❝❛✱ q✉❡r s♦❜ ❛ ♣❡rs♣❡❝t✐✈❛ ❞❡ ✉♠❛ ❝❛rt❡✐r❛ ❛❜❡rt❛✱ r❡❝♦rr❡♥❞♦ ❛♦ ▼♦❞❡❧♦ ❞♦s ❱órt✐❝❡s ❊st♦❝ást✐❝♦s ♣♦r ❡①❡♠♣❧♦✮✳ ◆❡st❛ ú❧t✐♠❛ ♣❡rs♣❡❝t✐✈❛ ❛❞♠✐t❡✲s❡ q✉❡ ❤á ❡♥tr❛❞❛s ❡ s❛í❞❛s ❞♦s s❡❣✉r❛❞♦s ❞❛ ❝❛rt❡✐r❛ ❞❛ s❡❣✉r❛❞♦r❛✱ t♦r♥❛♥❞♦✲s❡ ❛ss✐♠ ♠❛✐s r❡❛❧✐st❛✳

      ❊st✐♠❛r❛♠✲s❡✱ s♦❜ ❛♠❜❛s ❛s ♣❡rs♣❡❝t✐✈❛s✱ ❛s ❞✐str✐❜✉✐çõ❡s ❧✐♠✐t❡s ❛ss♦❝✐❛❞❛s ❛♦ SBM

      ❞❛ ●❛r❛♥t✐❛✱ ❜❡♠ ❝♦♠♦ ❛s ❊s❝❛❧❛s Ó♣t✐♠❛s ❞❡ Pré♠✐♦s ♣r♦♣♦st❛s ♣♦r ❛❧❣✉♥s ❛✉t♦r❡s ✭♥í✈❡❧ ♠é❞✐♦ r❡❧❛t✐✈♦ ❞❡ ❡st❛❝✐♦♥❛r✐❞❛❞❡✱ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✈❛r✐❛çã♦ ❞♦s ♣ré♠✐♦s✱ ❡❧❛st✐❝✐❞❛❞❡ ❞♦ ♣ré♠✐♦ ♠é❞✐♦ ❡ ❡❧❛st✐❝✐❞❛❞❡ tr❛♥s✐❡♥t❡✮✳

      ❯♠❛ ✈❡③ q✉❡ ♦ SBM ❡♠ ✈✐❣♦r ♥❛ ●❛r❛♥t✐❛ ♥ã♦ é ✉♠ s✐st❡♠❛ ❡✜❝✐❡♥t❡ ❛✈❛❧✐♦✉✲s❡ t❛♠❜é♠ ❞❡ ❢♦r♠❛ ❝♦♠♣❛r❛t✐✈❛ ✉♠❛ ❛❧t❡r❛çã♦ ❛♦ SBM ♣r♦♣♦st❛ ♣♦r ❉❛ ❛♥á❧✐s❡ ❡❢❡❝t✉❛❞❛ ❛♦s s✐st❡♠❛s ❞❡ ❜♦♥✉s ♠❛❧✉s ❡st✉❞❛❞♦s✱ ✉s❛♥❞♦ ♦s ❞❛❞♦s ❞❛

      ●❛r❛♥t✐❛✱ ❛ ♣r✐♥❝✐♣❛❧ ❝♦♥❝❧✉sã♦ é q✉❡ ❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦ ❡♥tr❡ ❛s ❝❧❛ss❡s ❞❡ ❜♦♥✉s ❞♦ s✐st❡♠❛ ❛❝t✉❛❧ sã♦ ❝♦♥tr❛❞✐tór✐❛s✳ ❊st❛s r❡❣r❛s ♥ã♦ r❡✢❡❝t❡♠ ✉♠ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❥✉st♦ ❡ ❢♦♠❡♥t❛♠ ❛ ❞❡❝❧❛r❛çã♦ ❞❡ s✐♥✐str♦s ❞❡ ♠♦❞♦ ❛ r❡❞✉③✐r ♦ ❛❣r❛✈❛♠❡♥t♦ ❞♦ ♣ré♠✐♦✳ ❈♦♠♦ ❥á ❢♦✐ r❡❢❡r✐❞♦✱ ♣❛r❛ ✉♠ s❡❣✉r❛❞♦ q✉❡ s❡ ❡♥❝♦♥tr❡ ♥❛ ❝❧❛ss❡ ❝♦♠ ✶✵✵✪ ❞❡ ❛❣r❛✈❛♠❡♥t♦ r❡✈❡❧❛✲s❡ s❡r ♠❛✐s ✈❛♥t❛❥♦s♦ ♣❛rt✐❝✐♣❛r ✉♠ s✐♥✐str♦ ♥❛ ❛♥✉✐❞❛❞❡ s❡❣✉✐♥t❡ ❞♦ q✉❡ ♥ã♦ ♣❛rt✐❝✐♣❛r ♥❡♥❤✉♠✳ ❙♦❜ ♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞❛ ❙❡❣✉r❛❞♦r❛✱ ✐st♦ ✐♠♣❧✐❝❛ ♦ ♣❛❣❛♠❡♥t♦ ❞❡ ♠❛✐s ✉♠❛ ✐♥❞❡♠♥✐③❛çã♦✱ ❜❡♠ ❝♦♠♦ ❛ r❡❞✉çã♦ ❞♦ ♣ré♠✐♦ ❛♦ s❡❣✉r❛❞♦ ♥❛ ❛♥✉✐❞❛❞❡ s❡❣✉✐♥t❡✳ P❛r❛ r❡s♦❧✈❡r ❡st❡s ♣r♦❜❧❡♠❛s✱ ♦ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ❛❧t❡r♥❛t✐✈♦ ❛♣r❡s❡♥t❛❞♦ ♣♦r ♣♦❞❡r✐❛ s❡r ✉♠❛ ❜♦❛ ❛❧t❡r♥❛t✐✈❛ ♥♦ ❢✉t✉r♦✱ ✈✐st♦ q✉❡ ❡♠ t❡r♠♦s ❞❡ tr❛♥s✐çã♦ ❡♥tr❡ ❡ss❡s ❞♦✐s s✐st❡♠❛s ♥ã♦ ❝❛✉s❛r✐❛ ❣r❛♥❞❡s tr❛♥st♦r♥♦s✱ ❞❛❞♦ q✉❡ ♦s ❞❡s❝♦♥t♦s ❡ ❛❣r❛✈❛♠❡♥t♦s ❝♦♥t✐♥✉❛r✐❛♠ ❛ s❡r ♦s ♠❡s♠♦s✱ ♠✉❞❛♥❞♦ ❛♣❡♥❛s ❛s r❡❣r❛s ❞❡ tr❛♥s✐çã♦ ❡♥tr❡ ❛s ❝❧❛ss❡s✱ ❡ ❝♦♥tr✐❜✉✐r✐❛ ♣❛r❛ ✉♠ s✐st❡♠❛ ❞❡ ❜♦♥✉s ♠❛❧✉s ♠❛✐s ❥✉st♦ ❡ ❡✜❝✐❡♥t❡ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞❛ s❡❣✉r❛❞♦r❛✳ ❊s♣❡r❛✲s❡ q✉❡ ❡st❡ tr❛❜❛❧❤♦ ♣♦ss❛

      ♦

      ❝♦♥tr✐❜✉✐r ♣❛r❛ ❛ ❛❧t❡r❛çã♦ ❞❛ ❧❡❣✐s❧❛çã♦✱ ♥♦♠❡❛❞❛♠❡♥t❡ ♦ ❉❡❝r❡t♦✲▲❡✐ ♥ ✶✼✴✷✵✵✸✱ q✉❡ ❡st❛❜❡❧❡❝❡ ♦ ❛❝t✉❛❧ SBM✱ ♣♦r ❢♦r♠❛ ❛ ❞❡✜♥✐r ✉♠ SBM ♠❛✐s ❡q✉✐❧✐❜r❛❞♦✳

      ❆❧❣✉♥s ❛s♣❡❝t♦s ♥ã♦ ❢♦r❛♠ ❛♥❛❧✐s❛❞❛s ♥♦ ❞❡❝♦rr❡r ❞❡st❡ tr❛❜❛❧❤♦✱ ♣♦❞❡♥❞♦ s❡r ❡s✲ t✉❞❛❞♦s ❡♠ tr❛❜❛❧❤♦s ❢✉t✉r♦s✱ ♥♦♠❡❛❞❛♠❡♥t❡✱ ♦ ❝á❧❝✉❧♦ ❞♦ ♥í✈❡❧ ❞❡ r❡t❡♥çã♦ ó♣t✐♠♦

      ✼✻ ❈❛♣ít✉❧♦ ✸✳ ❆♣❧✐❝❛çã♦ ❛♦s ❞❛❞♦s ❞❛ s❡❣✉r❛❞♦r❛ ●❛r❛♥t✐❛ ♠❡♥♦ ❡ ❛ r❡❛❧✐③❛çã♦ ❞❡ ♠❛✐s t❡st❡s ❡st❛tíst✐❝♦s ♥♦ ♠♦❞❡❧♦ ❞♦s ✈órt✐❝❡s ❡st♦❝ást✐❝♦s✳ ◆♦t❡✲s❡ q✉❡✱ ♣❛r❛ ❛ ❜♦❛ ❛♣❧✐❝❛çã♦ ❞❡ ❛❧❣✉♥s ❞❡st❡s t❡st❡s s❡r✐❛ ♥❡❝❡ssár✐❛ ❛ ♦❜t❡♥çã♦ ❞❡ ✐♥❢♦r♠❛çã♦ ❝♦♠ ✉♠ ♠❛✐♦r ❤♦r✐③♦♥t❡ t❡♠♣♦r❛❧ ❡ ♠❛✐s ❞❡t❛❧❤❛❞❛✱ ♣♦r ♣❛rt❡ ❞❛ s❡✲ ❣✉r❛❞♦r❛✱ r❡❧❛t✐✈❛♠❡♥t❡ ❛♦s ♠♦✈✐♠❡♥t♦s ❞❡ ❝❛rt❡✐r❛✳ ❆ ❛✉sê♥❝✐❛ ❞❡st❛ ✐♥❢♦r♠❛çã♦ ✐♠♣♦ss✐❜✐❧✐t♦✉ ❛ ❛♥á❧✐s❡ ❝♦♠ ♠❛✐s r✐❣♦r ❡st❛s q✉❡stõ❡s✳ ◆❛ ❡✈❡♥t✉❛❧✐❞❛❞❡ ❞❡ ♦❜t❡♥çã♦ ❞❡ ❞❛❞♦s ❡✱ s♦❜ ❛ ❤✐♣ót❡s❡ ❞❡ ✈❡r✐✜❝❛çã♦ ❞❛s ❝♦♥❞✐çõ❡s ♥❡❝❡ssár✐❛s✱ ✈❡r r❡ss❛❧t❛✲s❡ q✉❡ é ♣♦ssí✈❡❧ ♦❜t❡r ✐♥t❡r✈❛❧♦s ❞❡ ❝♦♥✜❛♥ç❛ ♣❛r❛ ❛ ❞✐str✐❜✉✐çã♦ ❧✐♠✐t❡ ❞♦ ♠♦❞❡❧♦ ❛❜❡rt♦✱ ♦ q✉❡ s❡ tr❛❞✉③✐r✐❛ ❡♠ ✐♥t❡r✈❛❧♦s ❞❡ ❝♦♥✜❛♥ç❛ ♣❛r❛ ❛s ❡s❝❛❧❛s ó♣t✐✲ ♠❛s ❞❡ ♣ré♠✐♦s✱ ♦ q✉❡ ♣♦r s✉❛ ✈❡③ tr❛♥s♠✐t❡ ❛❧❣✉♠❛ ✐♥❢♦r♠❛çã♦ ❡st❛tíst✐❝❛ ❛q✉❛♥❞♦ ❞❛ ✜①❛çã♦ ❞❛ ❡s❝❛❧❛ ❝♦♠❡r❝✐❛❧ ❛ ❛❞♦♣t❛r✳

      ❇✐❜❧✐♦❣r❛✜❛

      ❆♥❞r❛❞❡ ❡ ❙✐❧✈❛✱ ❏✳ ✭✶✾✾✶✮✳ ❊str✉t✉r❛s ❚❛r✐❢ár✐❛s ♥♦s ❘❛♠♦s ❘❡❛✐s ❞❛ ■♥❞ústr✐❛ ❙❡✲ ❣✉r❛❞♦r❛ ✲ ❯♠❛ ❛♣❧✐❝❛çã♦ ❛♦ s❡❝t♦r ❛✉t♦♠ó✈❡❧ ❡♠ P♦rt✉❣❛❧✳ ■♥st✐t✉t♦ ❙✉♣❡r✐♦r ❞❡ ❊❝♦♥♦♠✐❛ ❡ ●❡stã♦✱ ❯♥✐✈❡rs✐❞❛❞❡ ❚é❝♥✐❝❛ ❞❡ ▲✐s❜♦❛✳

      ❇♦r❣❛♥✱ ❖✳✱ ❍♦❡♠✱ ❏✳✱ ❡ ◆♦r❜❡r❣✱ ❘✳ ✭✶✾✽✶✮✳ ❆ ♥♦♥ ❛s②♠♣t♦t✐❝ ❝r✐t❡r✐♦♥ ❢♦r t❤❡ ❡✈❛❧✉❛t✐♦♥ ♦❢ ❛✉t♦♠♦❜✐❧❡ ❜♦♥✉s ♠❛❧✉s✳ ❙❝❛♥❞✐♥❛✈✐❛♥ ❆❝t✉❛r✐❛❧ ❏♦✉r♥❛❧✱ ♣❛❣❡s ✶✻✺✕ ✶✼✽✳

      ❇♦✇❡rs✱ ◆✳✱ ●❡r❜❡r✱ ❍✳✱ ❍✐❝❦♠❛♥✱ ❏✳✱ ❏♦♥❡s✱ ❉✳✱ ❡ ◆❡s❜✐tt✱ ❏✳ ✭✶✾✽✻✮✳ ❆❝t✉❛r✐❛❧ ▼❛t❤✲ ❡♠❛t✐❝s✳ ❚❤❡ ❙♦❝✐❡t② ♦❢ ❆❝t✉❛r✐❡s✳

      ❈❡♥t❡♥♦✱ ▲✳ ❡ ❆✳❙✐❧✈❛✱ ❏✳ ✭✷✵✵✷✮✳ ❖♣t✐♠❛❧ ❜♦♥✉s s❝❛❧❡s ✉♥❞❡r ♣❛t❤✲❞❡♣❡♥❞❡♥t ❜♦♥✉s r✉❧❡s✳ ❙❝❛♥❞✐♥❛✈✐❛♥ ❆❝t✉❛r✐❛❧ ❏♦✉r♥❛❧✱ ✷✿✶✷✾✕✶✸✻✳ ❈❡♥t❡♥♦✱ ▼✳ ✭✷✵✵✸✮✳ ❚❡♦r✐❛ ❞❡ ❘✐s❝♦ ♥❛ ❆❝t✐✈✐❞❛❞❡ s❡❣✉r❛❞♦r❛✳ ❈❡❧t❛ ❊❞✐t♦r❛✳ ❋❡❧❧❡r✱ ❲✳ ✭✶✾✻✻✮✳ ❆♥ ■♥tr♦❞✉❝t✐♦♥ t♦ Pr♦❜❛❜✐❧✐t② ❚❤❡♦r② ❛♥❞ ✐t✬s ❛♣♣❧✐❝❛t✐♦♥s✱ 2 nd

      ❊❞✐t✐♦♥✳ ❏♦❤♥ ❲✐❧❡② ❛♥❞ ❙♦♥s✱ ■♥❝✳ ●✐❧❞❡✱ ❱✳ ❡ ❙✉♥❞t✱ ❇✳ ✭✶✾✽✾✮✳ ❖♥ ❜♦♥✉s s②st❡♠s ✇✐t❤ ❝r❡❞✐❜✐❧✐t② s❝❛❧❡s✳ ❙❝❛♥❞✐♥❛✈✐❛♥

      ❆❝t✉❛r✐❛❧ ❏♦✉r♥❛❧✱ ✷✿✶✸✕✷✷✳ ●r❛♥❞❡❧❧✱ ❏✳ ✭✶✾✾✼✮✳ ▼✐①❡❞ P♦✐ss♦♥ Pr♦❝❡ss❡s✳ ❈❤❛♣♠❛♥ ✫ ❍❛❧❧✳ ●✉❡rr❡✐r♦✱ ●✳ ✭✷✵✵✶✮✳ ❯♠❛ ❆❜♦r❞❛❣❡♠ ❆❧t❡r♥❛t✐✈❛ ♣❛r❛ ❇♦♥✉s ▼❛❧✉s✳ ❚❡s❡ ❞❡

      ♠❡str❛❞♦✱ ■♥st✐t✉t♦ ❙✉♣❡r✐♦r ❞❡ ❊❝♦♥♦♠✐❛ ❡ ●❡stã♦✱ ❯♥✐✈❡rs✐❞❛❞❡ ❚é❝♥✐❝❛ ❞❡ ▲✐s❜♦❛✳ ●✉❡rr❡✐r♦✱ ●✳ ✭✷✵✵✽✮✳ P♦♣✉❧❛çõ❡s ❙✉❥❡✐t❛s ❛ ❘❡❝❧❛ss✐✜❝❛çõ❡s P❡r✐ó❞✐❝❛s✳ ❚❡s❡ ❞❡

      ❞♦✉t♦r❛♠❡♥t♦✱ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛✱ ❯♥✐✈❡rs✐❞❛❞❡ ◆♦✈❛ ❞❡ ▲✐s❜♦❛✳ ●✉❡rr❡✐r♦✱ ●✳ ❡ ▼❡①✐❛✱ ❏✳ ✭✷✵✵✹✮✳ ❆♥ ❛❧t❡r♥❛t✐✈❡ ❛♣♣r♦❛❝❤ t♦ ❜♦♥✉s ♠❛❧✉s✳ ❉✐s❝✉ss✐♦♥❡s

      ▼❛t❤❡♠❛t✐❝❛❡✱ Pr♦❜❛❜✐❧✐t② ❛♥❞ ❙t❛t✐st✐❝s✱ ✷✹✭✷✮✿✶✾✼✕✷✶✸✳ ●✉❡rr❡✐r♦✱ ●✳ ❡ ▼❡①✐❛✱ ❏✳ ✭✷✵✵✽✮✳ ❙t♦❝❤❛st✐❝ ✈♦rt✐❝❡s ✐♥ ♣❡r✐♦❞✐❝❛❧❧② r❡❝❧❛ss✐✜❡❞ ♣♦♣✉✲

      ✼✽ ❇■❇▲■❖●❘❆❋■❆

      ●✉❡rr❡✐r♦✱ ●✳✱ ▼❡①✐❛✱ ❏✳✱ ❡ ▼✐❣✉❡♥s✱ ▼✳ ✭✷✵✶✵✮✳ ❆ ♠♦❞❡❧ ❢♦r ♦♣❡♥ ♣♦♣✉❧❛t✐♦♥s s✉❜❥❡❝t t♦ ♣❡r✐♦❞✐❝❛❧ r❡✲❝❧❛ss✐✜❝❛t✐♦♥s✳ ❏♦✉r♥❛❧ ♦❢ ❙t❛t✐st✐❝❛❧ ❚❤❡♦r② ❛♥❞ Pr❛❝t✐❝❡✱ ✹✭✷✮✿✸✵✸✕ ✸✷✶✳

      ▲❡♠❛✐r❡✱ ❏✳ ✭✶✾✾✺✮✳ ❇♦♥✉s✲▼❛❧✉s ❙②st❡♠s ✐♥ ❆✉t♦♠♦❜✐❧❡ ■♥s✉r❛♥❝❡✳ ❑❧✉✇❡r ❆❝❛❞❡♠✐❝ P✉❜❧✐s❤❡rs✳

      ▲♦✐♠❛r❛♥t❛✱ ❑✳ ✭✶✾✼✷✮✳ ❙♦♠❡ ❛s②♠♣t♦t✐❝ ♣r♦♣❡rt✐❡s ♦❢ ❜♦♥✉s ♠❛❧✉s✳ ❆st✐♥ ❇✉❧❧❡t✐♥✱ ✻✿✷✸✸✕✷✹✺✳

      ▼❡①✐❛✱ ❏✳ ✭✷✵✵✵✮✳ ❱órt✐❝❡s ❊st♦❝ást✐❝♦s ❞❡ P❛râ♠❡tr♦ ❉✐s❝r❡t♦✳ P❤❉ t❤❡s✐s✱ ❈♦♠✉♥✐✲ ❝❛çã♦ ♥♦s ■■■ ❈♦❧óq✉✐♦s ❆❝t✉❛r✐❛✐s ❋❈❚✲❯◆▲✳

      ◆♦r❜❡r❣✱ ❘✳ ✭✶✾✼✻✮✳ ❆ ❝r❡❞✐❜✐❧✐t② t❤❡♦r② ❢♦r ❛✉t♦♠♦❜✐❧❡ ❜♦♥✉s ♠❛❧✉s✳ ❙❝❛♥❞✐♥❛✈✐❛♥ ❆❝t✉❛r✐❛❧ ❏♦✉r♥❛❧✱ ♣❛❣❡s ✾✷✕✶✵✼✳

      ❖sór✐♦✱ ❱✳ ✭✷✵✵✻✮✳ ❖ ❙❡❣✉r♦ ❖❜r✐❣❛tór✐♦ ❞❡ ❘❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❈✐✈✐❧ ❆✉t♦♠ó✈❡❧✳ ■♥st✐t✉t♦ ❞❛ ❇✐❜❧✐♦t❡❝❛ ❡ ❞♦ ▲✐✈r♦✳

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