❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦
❊s❝♦❧❛ ❙✉♣❡r✐♦r ❞❡ ❆❣r✐❝✉❧t✉r❛ ✏▲✉✐③ ❞❡ ◗✉❡✐r♦③✑
❊st✉❞♦ ❞❛ ✈♦❧❛t✐❧✐❞❛❞❡ ❞❛ sér✐❡ ❞❡ ♣r❡ç♦s ❞❛ s♦❥❛ ♣♦r ♠❡✐♦ ❞❡
♠♦❞❡❧♦s ●❆❘❈❍ ❡ ♠♦❞❡❧♦s ❆❘❋■▼❆
●❛❜r✐❡❧ ❚❛♠❜❛r✉ss✐ ❆✈❛♥❝✐♥✐
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s✳ ➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ❊st❛tís✲ t✐❝❛ ❡ ❊①♣❡r✐♠❡♥t❛çã♦ ❆❣r♦♥ô♠✐❝❛
●❛❜r✐❡❧ ❚❛♠❜❛r✉ss✐ ❆✈❛♥❝✐♥✐ ❇❛❝❤❛r❡❧ ❡♠ ▼❛t❡♠át✐❝❛
❊st✉❞♦ ❞❛ ✈♦❧❛t✐❧✐❞❛❞❡ ❞❛ sér✐❡ ❞❡ ♣r❡ç♦s ❞❛ s♦❥❛ ♣♦r ♠❡✐♦ ❞❡ ♠♦❞❡❧♦s ●❆❘❈❍ ❡ ♠♦❞❡❧♦s ❆❘❋■▼❆
✈❡rsã♦ r❡✈✐s❛❞❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ r❡s♦❧✉çã♦ ❈♦P●r ✻✵✶✽ ❞❡ ✷✵✶✶
❖r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ❱■❚❖❘ ❆❯●❯❙❚❖ ❖❩❆❑■
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s✳ ➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ❊st❛tíst✐❝❛ ❡ ❊①♣❡r✐✲ ♠❡♥t❛çã♦ ❆❣r♦♥ô♠✐❝❛
Dados Internacionais de Catalogação na Publicação DIVISÃO DE BIBLIOTECA - DIBD/ESALQ/USP
Avancini, Gabriel Tambarussi
Estudo de volatilidade da série de preços da soja por meio de modelos GARCH e modelos ARFIMA / Gabriel Tambarussi Avancini. - - versão revisada de acordo com a resolução CoPGr 6018 de 2011. - - Piracicaba, 2015.
99 p. : il.
Dissertação (Mestrado) - - Escola Superior de Agricultura “Luiz de Queiroz”.
1. Memória longa 2. Volatilidade 3. Retornos 4. Retornos absolutos 5. ARFIMA 6. GARCH I. Título
CDD 338.13334 A946e
✸
❉❊❉■❈❆❚Ó❘■❆
❆♦s ♠❡✉s ♣❛✐s✱
❆♣❛r❡❝✐❞❛ ❆❧✐❝❡ ❚❛♠❜❛r✉ss✐ ❡ ❙✐❧✈✐♦ ❘♦s❝❤❡❧ ❆✈❛♥❝✐♥✐ ♣❡❧♦ ❡①❡♠♣❧♦ ❞❡ ✈✐❞❛✱ ♣♦r ❡st❛r❡♠ s❡♠♣r❡ ❛♦ ♠❡✉ ❧❛❞♦ s❡♠♣r❡ ❞❛♥❞♦ ❢♦rç❛s q✉❛♥❞♦ ♣r❡❝✐s❡✐ ❡ ♣♦r ❛❝r❡❞✐t❛r❡♠ ♠❛✐s ❡♠ ♠✐♠ ❞♦ q✉❡ ❡✉ ♠❡s♠♦✳
➚ ♠✐♥❤❛ ♥❛♠♦r❛❞❛✱
❉é❜♦r❛ ❘♦❜❡rt ❞❡ ●♦❞♦✐
✺
❆●❘❆❉❊❈■▼❊◆❚❖❙
❆♦s ♠❡✉s ♣❛✐s✱ ❆♣❛r❡❝✐❞❛ ❆❧✐❝❡ ❚❛♠❜❛r✉ss✐ ❡ ❙✐❧✈✐♦ ❘♦s❝❤❡❧ ❆✈❛♥❝✐♥✐✱ ♣♦r s❡♠♣r❡ ♠❡ ✐♥❝❡♥t✐✈❛r❡♠ ❡ ♥✉♥❝❛ t❡r❡♠ ♠❡❞✐❞♦ ❡s❢♦rç♦s ♣❛r❛ q✉❡ ♠❡✉s s♦♥❤♦s s❡ r❡❛❧✐③❛ss❡♠ ❡ ♦❜✈✐❛♠❡♥t❡✱ ♣♦r s❡r❡♠ ♠❡✉s ❡①❡♠♣❧♦s ❞❡ ✈✐❞❛✳ ❖❜r✐❣❛❞♦ ♣♦r t✉❞♦✱ ❛♠♦ ♠✉✐t♦ ✈♦❝ês✦
❆♦s ♠❡✉s t✐♦s✱ ▼❛r✐❛ ■♥ês ❡ ❈❛r❧♦s ❊❞✉❛r❞♦✱ ❡ t❛♠❜é♠ ❛♦ ♠❡✉ ♣r✐♠♦✴✐r♠ã♦ ❉✉❞s q✉❡ s❡♠♣r❡ t✐✈❡r❛♠ ♣❛❝✐ê♥❝✐❛ ❝♦♠✐❣♦ ❡ ❝♦♥tr✐❜✉ír❛♠ ♠✉✐t♦ ♣❛r❛ ♠❡✉ ❝r❡s❝✐♠❡♥t♦✦
❆♦ ♠❡✉ t✐♦ ❈❡❧s♦ ❘♦s❝❤❡❧ ❆✈❛♥❝✐♥✐✱ q✉❡ s❡♠♣r❡ ♠❡ ❛❥✉❞♦✉ ♥♦s ♠♦♠❡♥t♦s ❞✐❢í❝❡✐s ❞❛ ✈✐❞❛ ❡ s❡♠♣r❡ ♠❡ ❛❝♦❧❤❡✉ ❞❛ ♠❡❧❤♦r ♠❛♥❡✐r❛ ♣♦ssí✈❡❧✦ ❱♦❝ê ❥á ♠❡ ❛❥✉❞♦✉ ♠✉✐t♦✱ ♠✉✐t♦ ♠❡s♠♦✦ ❖❜r✐❣❛❞♦✦
❆♦ ♠❡✉ ✐r♠ã♦✱ P❡❞r♦ ▲✉✐③ ▼❛♥❛❝❡r♦ ❆✈❛♥❝✐♥✐✱ ❛q✉❡❧❡ ✐r♠ã♦③✐♥❤♦ q✉❡ ❙❊▼P❘❊ q✉✐s t❡r✦
❆♦ ♠❡✉ ❣r❛♥❞❡ ❛♠♦r✱ ❉é❜♦r❛ ❘♦❜❡rt ❞❡ ●♦❞♦✐✱ ♣♦r ♥✉♥❝❛ ♠❡ ❞❡✐①❛r ❞❡s✐st✐r✱ ♣♦r ❡st❛r s❡♠♣r❡ ❛♦ ♠❡✉ ❧❛❞♦✱ ♠❡ ❢❛③❡♥❞♦ ❝❛❞❛ ❞✐❛ ♠❛✐s ❢❡❧✐③✦ ❊✉ t❡ ❆▼❖ ▼❯■❚❖✦✦✦
❆♦ Pr♦❢✳ ❉r✳ ❱✐t♦r ❆✉❣✉st♦ ❖③❛❦✐✱ ♣❡❧❛ ♦r✐❡♥t❛çã♦✱ ❝♦♥✜❛♥ç❛ ❡ ✐♥❝❡♥t✐✈♦ ❞❛❞♦ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳
➚ Pr♦❢a ❉r❛✳ ❊❧ír✐s ❈r✐st✐♥❛ ❘✐③③✐♦❧✐ ♣r♦❢❡ss♦r❛ ❞❡ ❣r❛❞✉❛çã♦ ❡ ♦r✐❡♥t❛❞♦r❛ ♥❡st❡ ♣❡rí♦❞♦✱ q✉❡ ❛❧é♠ ❞❡ t♦❞♦s ❡♥s✐♥❛♠❡♥t♦s ❛❝❛❞ê♠✐❝♦s s❡ t♦r♥♦✉ ❣r❛♥❞❡ ❛♠✐❣❛✳
❆♦ Pr♦❢✳ ❉r✳ ❆♥tô♥✐♦ ❈❛r❧♦s ❙✐♠õ❡s P✐ã♦ ♣r♦❢❡ss♦r q✉❡ ♠❡ ✐♥❝❡♥t✐✈♦✉ ❛ ♣r♦ss❡❣✉✐r ❝♦♠ ♦s ❡st✉❞♦s ✐♥❞✐❝❛♥❞♦ ❛ ❊❙❆▲◗✳
➚ ❢❛♠í❧✐❛ ❙♦❜r❡✈✐✈❡✱ ◆❡✐rs♦✱ ◆✐❧t✐♥❤♦✱ ❘❛❢❛✱ ▼❛✉▼❛✉✱ P✐♥t♦✱ ❊❞✐✱ Pr✐♠♦✱ ❆❧ê✱ P❡❞rã♦✱ ❮❧✐♦✱ ❡ ❘❛♠❜♦ ✭❞♦❣✦✮ ♣❡ss♦❛s ❝♦♠ ❛s q✉❛✐s ✈✐✈✐ ♥❛ ♠❡s♠❛ r❡♣ú❜❧✐❝❛✱ ❡ q✉❡ ✜③❡r❛♠ ♣❛rt❡ ❞❛ ♠❡❧❤♦r ❢❛s❡ ❞❡ ♠✐♥❤❛ ✈✐❞❛✱ q✉❡ ♠❡ ♣r♦♣♦r❝✐♦♥❛r❛♠ ✐♥ú♠❡r♦s ♠♦♠❡♥t♦s ✐♥❡sq✉❡❝í✈❡✐s ❡ q✉❡ ❞❡✈❡♠ ✜❝❛r ❣✉❛r❞❛❞♦s ❛♣❡♥❛s ♥❛ ♠❡♠ór✐❛ ❡ ♥ã♦ ❡s❝r✐t♦s✦✦✦
❆♦s ♠❡✉s ❛♠✐❣♦s ❡ t✉r♠❛ ❞❡ ♠❡str❛❞♦✴❞♦✉t♦r❛❞♦✱ P❡❞r♦✱ ❉❥❛✐r✱ ▼❛r❝❡❧♦✱ ❑❧❡✐♥✱ ❘❡❣✐♥❛❧❞♦✱ ▼❛r❝✉s✱ ❊❧✐❛s✱ ❚❤✐❛❣♦✱ ❘❛❢❛✱ ❙✐♠♦♥❡✱ ❚❤✐❛❣♦ ✭❜❡♠✮✱ ❉✐❣ã♦ ❡ P❡❞rã♦ ♣♦r ❡ss❡s ❛♥♦s ❞❡ ❡st✉❞♦ ❡ ❞❡ ♠✉✐t♦s ❝❛❢és✦✦✦
❆♦ ❉✐❡❣♦ ❇✐s✐♥♦t♦✱ ♣♦r ❡♥t❡♥❞❡r ❛s ❞✐✜❝✉❧❞❛❞❡s✱ ♠❡ ❛❥✉❞❛r✱ ❡ ♠❡ ❞❡✐①❛r ❧✐✈r❡ ♣❛r❛ ❢♦❧❣❛r ♥♦s ❢❡r✐❛❞♦s q✉❡ ♣r❡❝✐s❡✐✳
✻
❆♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❞❛ ❊❙❆▲◗✱ ❡♠ ❡s♣❡❝✐❛❧✱ à ▲✉❝✐❛♥❡ ❇r❛❥ã♦ ♣♦r t♦❞❛ ❛❥✉❞❛ s❡♠♣r❡ q✉❡ ♣r❡❝✐s❡✐✦
✼
✏❙❡ ✈♦❝ê ♣♦❞❡ s♦♥❤❛r✱ ✈♦❝ê ♣♦❞❡ ❢❛③❡r✳✑
❲❛❧t ❉✐s♥❡②
✏❊✉ t❡♥t❡✐ ✾✾ ✈❡③❡s ❡ ❢❛❧❤❡✐✱ ♠❛s ♥❛ ❝❡♥tés✐♠❛ t❡♥t❛t✐✈❛ ❡✉ ❝♦♥s❡❣✉✐✱ ♥✉♥❝❛ ❞❡s✐st❛ ❞❡ s❡✉s ♦❜❥❡t✐✈♦s ♠❡s♠♦ q✉❡ ❡ss❡s ♣❛r❡ç❛♠ ✐♠♣♦ssí✈❡✐s✱ ❛ ♣ró①✐♠❛ t❡♥t❛t✐✈❛ ♣♦❞❡ s❡r ❛ ✈✐t♦r✐♦s❛✳✑
✽
✾
❙❯▼➪❘■❖
❘❊❙❯▼❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ❆❇❙❚❘❆❈❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✶ ■◆❚❘❖❉❯➬➹❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷ ❘❊❱■❙➹❖ ❇■❇▲■❖●❘➪❋■❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✶ ❈♦♠♠♦❞✐t✐❡s ❛❣rí❝♦❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✷ ❆ s♦❥❛ ♥♦ ❇r❛s✐❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✸ ❊st✉❞♦s r❡❧❛❝✐♦♥❛❞♦s à ✈♦❧❛t✐❧✐❞❛❞❡ ❞❛ s♦❥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✹ ❙ér✐❡s t❡♠♣♦r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✺ ❊st❛❝✐♦♥❛r✐❡❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✻ ❋❛♠í❧✐❛ ❆❘■▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✻✳✶ ▼♦❞❡❧♦ ❛✉t♦rr❡❣r❡ss✐✈♦ ✲ ❆❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✻✳✷ ▼♦❞❡❧♦ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✲ ▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✻✳✸ ▼♦❞❡❧♦ ❛✉t♦rr❡❣r❡ss✐✈♦ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✲ ❆❘▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✻✳✹ ▼♦❞❡❧♦ ❛✉t♦rr❡❣r❡ss✐✈♦ ✐♥t❡❣r❛❞♦ ❡ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✲ ❆❘■▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✼ Pr♦❝❡ss♦s ❞❡ ♠❡♠ór✐❛ ❧♦♥❣❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✼✳✶ ▼♦❞❡❧♦ ❛✉t♦rr❡❣r❡ss✐✈♦ ❢r❛❝✐♦♥ár✐♦ ✐♥t❡❣r❛❞♦ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✲ ❆❘❋■▼❆ ✳ ✳ ✷✾ ✷✳✽ ▼♦❞❡❧♦s ❤❡t❡r♦s❝❡❞ást✐❝♦s ❝♦♥❞✐❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✽✳✶ ▼♦❞❡❧♦ ❛✉t♦rr❡❣r❡ss✐✈♦ ❝♦♠ ❤❡t❡r♦s❝❡❞❛st✐❝✐❞❛❞❡ ❝♦♥❞✐❝✐♦♥❛❧ ✲ ❆❘❈❍ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✽✳✶✳✶ ❉❡s✈❛♥t❛❣❡♥s ❞♦ ♠♦❞❡❧♦ ❆❘❈❍ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✽✳✷ ▼♦❞❡❧♦ ❛✉t♦rr❡❣r❡ss✐✈♦ ❣❡♥❡r❛❧✐③❛❞♦ ❝♦♠ ❤❡t❡r♦s❝❡❞❛st✐❝✐❞❛❞❡ ❝♦♥❞✐❝✐♦♥❛❧ ✲
●❆❘❈❍ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✽✳✷✳✶ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ♠♦❞❡❧♦s ❆❘▼❆ ❡ ●❆❘❈❍ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✸ ▼❆❚❊❘■❆▲ ❊ ▼➱❚❖❉❖❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✶ ❈♦♥❝❡✐t♦s ❜ás✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✶✳✶ ❘❡t♦r♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✳✶✳✷ ▼♦❞❡❧♦s ❛✉t♦rr❡❣r❡ss✐✈♦s ✲ ❆❘✭p✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✸✳✶✳✸ ▼♦❞❡❧♦s ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✲ ▼❆✭q✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
✸✳✶✳✹ ▼♦❞❡❧♦s ❛✉t♦rr❡❣r❡ss✐✈♦s ❡ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✲ ❆❘▼❆✭p, q✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✸✳✶✳✺ ▼♦❞❡❧♦s ❛✉t♦rr❡❣r❡ss✐✈♦s ✐♥t❡❣r❛❞♦s ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✲ ❆❘■▼❆✭p, d, q✮ ✳ ✳ ✳ ✳ ✹✹
✶✵
✸✳✷✳✶ ▼♦❞❡❧♦s ❛✉t♦rr❡❣r❡ss✐✈♦s ❢r❛❝✐♦♥ár✐♦s ✐♥t❡❣r❛❞♦s ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✲ ❆❘❋■▼❆✭p, d, q✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻
✸✳✷✳✷ ❚❡st❡s ❡st❛tíst✐❝♦s ♣❛r❛ ♣❛r❛ ♠❡♠ór✐❛ ❧♦♥❣❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✸✳✷✳✷✳✶ ❊st❛tíst✐❝❛ ❘✴❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✸✳✷✳✷✳✷ ❚❡st❡ ●P❍ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✷✳✸ ❊st✐♠❛çã♦ ❞♦ ♣❛râ♠❡tr♦ ❞❡ ♠❡♠ór✐❛ ❧♦♥❣❛ d ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✸✳✷✳✸✳✶ ❊st✐♠❛çã♦ ❞♦ ♣❛râ♠❡tr♦ d ♣♦r ♠❡✐♦ ❞❛ ❡st❛tíst✐❝❛ ❘✴❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✸✳✷✳✸✳✷ ❊st✐♠❛çã♦ ❞♦ ♣❛râ♠❡tr♦ d ♣❡❧♦ ♠ét♦❞♦ ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✺✷
✸✳✷✳✸✳✸ Pr❡✈✐sã♦ ❞❡ ♠♦❞❡❧♦s ❆❘❋■▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✸✳✸ ▼♦❞❡❧♦s ❤❡t❡r♦s❝❡❞ást✐❝♦s ❝♦♥❞✐❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✸✳✸✳✶ ▼♦❞❡❧♦s ❆✉t♦rr❡❣r❡ss✐✈♦s ❝♦♠ ❍❡t❡r♦s❝❡❞❛st✐❝✐❞❛❞❡ ❈♦♥❞✐❝✐♦♥❛❧ ✲ ❆❘❈❍ ✳ ✳ ✳ ✺✹ ✸✳✸✳✶✳✶ ❚❡st❡s ♣❛r❛ ❡❢❡✐t♦s ❆❘❈❍ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✸✳✸✳✶✳✶✳✶ ❚❡st❡ ▲❥✉♥❣✲❇♦① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✸✳✸✳✶✳✶✳✷ ❚❡st❡ ❞♦s ♠✉❧t✐♣❧✐❝❛❞♦r❡s ❞❡ ▲❛❣r❛♥❣❡ ✭LM✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✸✳✸✳✶✳✷ ❊st✐♠❛çã♦ ❞❡ ♠♦❞❡❧♦s ❆❘❈❍ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✸✳✸✳✶✳✸ ❱❡r✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸✳✸✳✶✳✹ Pr❡✈✐sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸✳✸✳✶✳✺ ▼♦❞❡❧♦s ❆❘❈❍ ●❡♥❡r❛❧✐③❛❞♦ ✲ ●❆❘❈❍ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✸✳✹ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♠♦❞❡❧♦s ❡ ♠❡❞✐❞❛ ❞❡ ♣r❡❝✐sã♦ ❞❛ ♣r❡✈✐sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✸✳✺ ❈♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹ ❘❊❙❯▲❚❆❉❖❙ ❊ ❉■❙❈❯❙❙➹❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✶ ❆♥á❧✐s❡ ♣r❡❧✐♠✐♥❛r ❞♦s ❞❛❞♦s ❡ ❞♦s r❡t♦r♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✷ ❊st✉❞♦ ❞❛ ✈♦❧❛t✐❧✐❞❛❞❡ ✉t✐❧✐③❛♥❞♦ ♦s r❡t♦r♥♦s ❛❜s♦❧✉t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✸ ❊st✐♠❛çã♦ ❡ ❞✐❛❣♥óst✐❝♦ ❞♦ ♠♦❞❡❧♦ ❆❘❋■▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✸✳✶ ▼ét♦❞♦ ❞❛ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✸✳✷ ❉✐❢❡r❡♥❝✐❛♥❞♦ ❛ sér✐❡ ♣♦r ✉♠ ✈❛❧♦r ❞❡ d ❡st✐♠❛❞♦ ❡ ❛❥✉st❛♥❞♦ ✉♠ ♠♦❞❡❧♦
❆❘▼❆✭p✱q✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
✹✳✸✳✷✳✶ P❛râ♠❡tr♦ d ❡st✐♠❛❞♦ ♣❡❧♦ ♠ét♦❞♦ ●P❍ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
✹✳✸✳✷✳✷ P❛râ♠❡tr♦ d ❡st✐♠❛❞♦ ♣❡❧♦ ♠ét♦❞♦ ❘✴❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
✶✶
❘❊❙❯▼❖
❊st✉❞♦ ❞❛ ✈♦❧❛t✐❧✐❞❛❞❡ ❞❛ sér✐❡ ❞❡ ♣r❡ç♦s ❞❛ s♦❥❛ ♣♦r ♠❡✐♦ ❞❡ ♠♦❞❡❧♦s ●❆❘❈❍ ❡ ♠♦❞❡❧♦s ❆❘❋■▼❆
❖ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ ❢♦✐ ❡st✉❞❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ ✈♦❧❛t✐❧✐❞❛❞❡ ❞♦ ♣r❡ç♦ ❞❛ s♦❥❛ ♥❡❣♦❝✐❛❞❛ ❡♠ ❝♦♥tr❛t♦s ❢✉t✉r♦s ♥❛ ❇▼✫❋❇❖❱❊❙P❆ ✭sér✐❡ ❙❋■✮✳ ❖ ❡st✉❞♦ ❢♦✐ r❡❛❧✐③❛❞♦ ♣♦r ♠❡✐♦ ❞❛ ❝♦♠♣❛r❛çã♦ ❡♥tr❡ ❞✉❛s ❛❜♦r❞❛❣❡♥s✿ ♥❛ ♣r✐♠❡✐r❛✱ ❢♦✐ ✉t✐❧✐③❛❞❛ ❛ sér✐❡ ❞❡ r❡t♦r♥♦s ❛❜s♦❧✉t♦s ❞❛ sér✐❡ ❡♠ q✉❡stã♦ ♣❛r❛ r❡♣r❡s❡♥t❛r ❛ ✈♦❧❛t✐❧✐❞❛❞❡ ❞❛ ♠❡s♠❛✱ q✉❡ s❡ ♠♦str♦✉ ♣❡rs✐st❡♥t❡ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✱ ❝♦♠♣r♦✈❛♥❞♦ ♦ ❢❛t♦ ❞❡ q✉❡ ❛ sér✐❡ ♣♦ss✉✐ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ♠❡♠ór✐❛ ❧♦♥❣❛✳ P♦r t❡r ❛♣r❡s❡♥t❛❞♦ t❛❧ ❝♦♠♣♦rt❛♠❡♥t♦✱ ❢❡③✲s❡ ♥❡❝❡ssár✐❛ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ♠♦❞❡❧♦s ❆❘❋■▼❆ ✭✏❆✉t♦rr❡❣r❡ss✐✈♦s ❋r❛❝✐♦♥ár✐♦s ■♥t❡❣r❛❞♦s ❞❡ ▼é❞✐❛s ▼ó✈❡✐s✑✮ ❡st❡s✱ q✉❡ sã♦ ❝❛♣❛③❡s ❞❡ ❝❛♣t✉r❛r ❞❡ ♠❛♥❡✐r❛ ❡❢❡t✐✈❛ t❛❧ ❝♦♠♣♦rt❛♠❡♥t♦✳ ❆✐♥❞❛ ❞❡♥tr♦ ❞❡st❛ ❛❜♦r❞❛❣❡♠✱ ♦s ♠♦❞❡❧♦s ❢♦r❛♠ ❡st✐♠❛❞♦s ❞❡ ❞✉❛s ♠❛♥❡✐r❛s ❞✐st✐♥t❛s✿ ❛ ♣r✐♠❡✐r❛✱ ❡♠ q✉❡ t♦❞♦s ♦s ♣❛râ♠❡tr♦s ❢♦r❛♠ ❡st✐♠❛❞♦s s✐♠✉❧t❛♥❡❛♠❡♥t❡ ❡ ❛ s❡❣✉♥❞❛✱ ❡♠ q✉❡ ♣r✐♠❡✐r❛♠❡♥t❡ ❢♦✐ ❡st✐♠❛❞♦ ♦ ♣❛râ♠❡tr♦ ❞❡ ♠❡♠ór✐❛ ❧♦♥❣❛✱ ❞✐❢❡r❡♥❝✐❛❞❛ ❛ sér✐❡ ❡✱ ♣♦st❡r✐♦r♠❡♥t❡✱ ❢♦r❛♠ ❛❥✉st❛❞♦s ♦s ♠♦❞❡❧♦s ❆❘■▼❆ ♥♦s ❞❛❞♦s ❞✐❢❡r❡♥❝✐❛❞♦s✳ P♦r ✜♠✱ ❛ s❡❣✉♥❞❛ ❛❜♦r❞❛❣❡♠ ✉t✐❧✐③❛❞❛ ♥♦ tr❛❜❛❧❤♦ é ❛ ♠❛✐s ❝♦♠✉♠ ❡♠ ♣❡sq✉✐s❛s ❛❝❛❞ê♠✐❝❛s✿ ❢♦✐ r❡❛❧✐③❛❞❛ ❛ ❡st✐♠❛çã♦ ❞♦s ♠♦❞❡❧♦s ●❆❘❈❍ ✭✏❆✉t♦rr❡❣r❡ss✐✈♦s ●❡♥❡r❛❧✐③❛❞♦s ❞❡ ❍❡t❡r♦s❝❡❞❛st✐❝✐❞❛❞❡ ❈♦♥❞✐❝✐♦♥❛❧✮ ❞✐r❡t❛♠❡♥t❡ ♥❛ sér✐❡ ❞❡ r❡t♦r♥♦s✳ ◆❡st❡ ❡st✉❞♦✱ ❝♦♥❝❧✉í♠♦s q✉❡ ❛ ♣r✐♠❡✐r❛ ❛❜♦r❞❛❣❡♠ s❡ ♠♦str♦✉ ♠❛✐s ❡✜❝✐❡♥t❡✱ ❞❛❞♦s ♦s ❝r✐tér✐♦s ❞❡ ❝♦♠♣❛r❛çã♦ ✉t✐❧✐③❛❞♦s✳
✶✸
❆❇❙❚❘❆❈❚
❱♦❧❛t✐❧✐t② ♦❢ s♦②❜❡❛♥ ♣r✐❝❡ r❛♥❣❡ ✉s✐♥❣ ●❆❘❈❍ ♠♦❞❡❧s ❛♥❞ ❆❘❋■▼❆ ♠♦❞❡❧s
❚❤❡ ♣✉r♣♦s❡ ♦❢ t❤✐s ❛rt✐❝❧❡ ✇❛s t♦ st✉❞② t❤❡ ✈♦❧❛t✐❧✐t② ♦❢ t❤❡ s♦②❜❡❛♥ ♣r✐❝❡ tr❛❞❡❞ ✐♥ ❢✉t✉r❡s ❝♦♥tr❛❝ts ♦♥ t❤❡ ❇▼✫❋❇❖❱❊❙P❆ ✭❙❋■ s❡r✐❡s✮✳ ❚❤❡ st✉❞② ✇❛s ❝♦♥❞✉❝t ❜② ❝♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ t✇♦ ❛♣♣r♦❛❝❤❡s✿ ✜rst✱ ✇❛s ✉s❡ t❤❡ s❡r✐❡s ♦❢ ❛❜s♦❧✉t❡ r❡t✉r♥s ♦❢ t❤❡ r❡s♣❡❝t✐✈❡ s❡r✐❡s✱ t♦ r❡♣r❡s❡♥t ✐ts ✈♦❧❛t✐❧✐t②✱ ✇❤✐❝❤ ✇❛s ♣❡rs✐st❡♥t ♦✈❡r t✐♠❡✱ ♣r♦✈✐♥❣ t❤❡ ❢❛❝t t❤❛t t❤❡ s❡r✐❡s ❤❛s ❛ ❧♦♥❣ ♠❡♠♦r② ❜❡❤❛✈✐♦r✳ ❇❡❝❛✉s❡ ♦❢ s✉❝❤ ❜❡❤❛✈✐♦r✱ ✐t ✇❛s ♥❡❝❡ss❛r② t♦ ✉s❡ ❆❘❋■▼❆ ♠♦❞❡❧s ✭✏❆✉t♦r❡❣r❡ss✐✈❡ ❋r❛❝t✐♦♥❛❧ ■♥t❡❣r❛t❡❞ ▼♦✈✐♥❣ ❆✈❡r❛❣❡✑✮✱ ✇❤✐❝❤ ❛r❡ ❛❜❧❡ t♦ ❝❛♣t✉r❡ ❡✛❡❝t✐✈❡❧② s✉❝❤ ❜❡❤❛✈✐♦r✳ ❙t✐❧❧ ✉s✐♥❣ t❤✐s ❛♣♣r♦❛❝❤✱ t❤❡ ♠♦❞❡❧s ✇❡r❡ ❡st✐♠❛t❡ ✐♥ t✇♦ ❞✐✛❡r❡♥t ✇❛②s✿ ✜rst✱ ✇❤✐❝❤ ❛❧❧ ♣❛r❛♠❡t❡rs ✇❡r❡ ❡st✐♠❛t❡ s✐♠✉❧t❛♥❡♦✉s❧②✱ ❛♥❞ t❤❡ s❡❝♦♥❞ ♦♥❡✱ t❤❛t ✇❛s ✜rst ❡st✐♠❛t❡❞ t❤❡ ❧♦♥❣ ♠❡♠♦r② ♣❛r❛♠❡t❡r✱ ❞✐✛❡r❡♥t✐❛t❡❞ t❤❡ s❡r✐❡s ❛♥❞✱ ❧❛t❡r✱ ❛❞❥✉st❡❞ t❤❡ ❆❘■▼❆ ♠♦❞❡❧s ✐♥ ❞✐✛❡r❡♥t✐❛t❡❞ ❞❛t❛✳ ❋✐♥❛❧❧②✱ t❤❡ s❡❝♦♥❞ ❛♣♣r♦❛❝❤ ✉s❡❞ ✐♥ t❤✐s ✇♦r❦ ✐s t❤❡ ♠♦st ❝♦♠♠♦♥ ✐♥ ❛❝❛❞❡♠✐❝ r❡s❡❛r❝❤✿ t❤❡ ❡st✐♠❛t✐♦♥ ♦❢ ●❆❘❈❍ ♠♦❞❡❧s ✭✏●❡♥❡r❛❧✐③❡❞ ❆✉t♦r❡❣r❡ss✐✈❡ ❈♦♥❞✐t✐♦♥❛❧ ❍❡r❡t♦s❝s❦❡❞❛st✐❝✐t②✑✮ ❞✐r❡❝t❧② ✐♥ t❤❡ r❡t✉r♥s s❡r✐❡s ♦❢ t❤❡ st✉❞✐❡❞ s❡r✐❡s✳ ■♥ t❤✐s st✉❞②✱ ✇❡ ❝♦♥❝❧✉❞❡ t❤❛t t❤❡ ✜rst ❛♣♣r♦❛❝❤ ✇❛s ♠♦r❡ ❡✛❡❝t✐✈❡✱ ❣✐✈❡♥ t❤❡ ❝♦♠♣❛r✐s♦♥ ❝r✐t❡r✐❛ ✉s❡❞✳
✶✺
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
❋✐❣✉r❛ ✶ ✲ ❢❛❝ ❡ ❢❛❝♣ ❞❡ ❞♦✐s ♣r♦❝❡ss♦s ❆❘✭✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ❋✐❣✉r❛ ✷ ✲ ❢❛❝ ❡ ❢❛❝♣ ❞❡ ❞♦✐s ♣r♦❝❡ss♦s ❆❘✭✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ❋✐❣✉r❛ ✸ ✲ ❢❛❝ ❡ ❢❛❝♣ ❞❡ ❞♦✐s ♣r♦❝❡ss♦s ▼❆✭✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ❋✐❣✉r❛ ✹ ✲ ❢❛❝ ❡ ❢❛❝♣ ❞❡ ❞♦✐s ♣r♦❝❡ss♦s ▼❆✭✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ❋✐❣✉r❛ ✺ ✲ ❢❛❝ ❡ ❢❛❝♣ ❞❡ ❞♦✐s ♣r♦❝❡ss♦s ❆❘▼❆✭✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ❋✐❣✉r❛ ✻ ✲ ❢❛❝ ❡ ❢❛❝♣ ❞❡ ✉♠ ♣r♦❝❡ss♦ ❆❘❋■▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ❋✐❣✉r❛ ✼ ✲ ✭❛✮ ❙ér✐❡ ❞♦ ♣r❡ç♦ ❞❛ s♦❥❛ ✭❜✮ ❙ér✐❡ ❞❡ r❡t♦r♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ❋✐❣✉r❛ ✽ ✲ ✭❛✮ ❍✐st♦❣r❛♠❛ ❞♦s r❡t♦r♥♦s ✭❜✮ ◗✲◗♣❧♦t ❞♦s r❡t♦r♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ❋✐❣✉r❛ ✾ ✲ ✭❛✮ ❙ér✐❡ ❞❡ r❡t♦r♥♦s ❛❜s♦❧✉t♦s ✭❜✮ ❋✉♥çã♦ ❞❡ ❛✉t♦❝♦rr❡❧❛çã♦ ❛♠♦str❛❧ ❞❛
sér✐❡ ❞❡ r❡t♦r♥♦s ❛❜s♦❧✉t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ❋✐❣✉r❛ ✶✵ ✲✭❛✮ ◗✲◗♣❧♦t ❞♦s r❡sí❞✉♦s ♣❛❞r♦♥✐③❛❞♦s ✭❜✮ ❆✉t♦❝♦rr❡❧❛çõ❡s ❞♦s r❡sí❞✉♦s ✻✾ ❋✐❣✉r❛ ✶✶ ✲✭❛✮ ❙ér✐❡ ❞❡ r❡t♦r♥♦s ❞✐❢❡r❡♥❝✐❛❞♦s ❝♦♠ d ❢r❛❝✐♦♥ár✐♦ ✭❚❡st❡ ●P❍✮ ✭❜✮
❆✉t♦❝♦rr❡❧❛çõ❡s ❞♦s r❡t♦r♥♦s ❞✐❢❡r❡♥❝✐❛❞♦s ✭❝✮ ❆✉t♦❝♦rr❡❧❛çõ❡s ♣❛r❝✐❛✐s ❞♦s r❡t♦r♥♦s ❞❡❢❡r❡♥❝✐❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ❋✐❣✉r❛ ✶✷ ✲✭❛✮ ◗✲◗♣❧♦t ❞♦s r❡sí❞✉♦s ♣❛❞r♦♥✐③❛❞♦s ✭❜✮ ❆✉t♦ ❝♦rr❡❧❛çõ❡s ❞♦s r❡sí❞✉♦s ✼✶ ❋✐❣✉r❛ ✶✸ ✲✭❛✮ ❙ér✐❡ ❞❡ r❡t♦r♥♦s ❞✐❢❡r❡♥❝✐❛❞♦s ❝♦♠ d ❢r❛❝✐♦♥ár✐♦ ✭▼ét♦❞♦ ❘✴❙✮ ✭❜✮
❆✉t♦❝♦rr❡❧❛çõ❡s ❞♦s r❡t♦r♥♦s ❞✐❢❡r❡♥❝✐❛❞♦s ✭❝✮ ❆✉t♦❝♦rr❡❧❛çõ❡s ♣❛r❝✐❛✐s ❞♦s r❡t♦r♥♦s ❞❡❢❡r❡♥❝✐❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ❋✐❣✉r❛ ✶✹ ✲✭❛✮ ◗✲◗♣❧♦t ❞♦s r❡sí❞✉♦s ♣❛❞r♦♥✐③❛❞♦s ✭❜✮ ❆✉t♦❝♦rr❡❧❛çõ❡s ❞♦s r❡sí❞✉♦s ✼✸ ❋✐❣✉r❛ ✶✺ ✲❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ✈♦❧❛t✐❧✐❞❛❞❡ ❡ sér✐❡ ❞❡ r❡t♦r♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ❋✐❣✉r❛ ✶✻ ✲✭❛✮ ❋✉♥çã♦ ❞❡ ❛✉t♦❝♦rr❡❧❛çã♦ ❞♦s r❡t♦r♥♦s ✭❜✮ ❋✉♥çã♦ ❞❡ ❛✉t♦❝♦rr❡❧❛çã♦
❞♦s q✉❛❞r❛❞♦s ❞♦s r❡t♦r♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ❋✐❣✉r❛ ✶✼ ✲✭❛✮ ❘❡sí❞✉♦s ♣❛❞r♦♥✐③❛❞♦s ✭❜✮ ❆✉t♦❝♦rr❡❧❛çõ❡s ❞♦s r❡sí❞✉♦s ✭❝✮ ❱❛❧♦r ❞❡
p ♦❜t✐❞♦ ✈✐❛ ❡st❛tíst✐❝❛s ▲❥✉♥❣✲❇♦① ✭❞✮ ❆✉t♦❝♦rr❡❧❛çã♦ ❞♦s q✉❛❞r❛❞♦s
✶✻
✶✼
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙
❚❛❜❡❧❛ ✶ ✲ ❈❛r❛❝t❡ríst✐❝❛s ❞♦ ♣❛râ♠❡tr♦ d ❢r❛❝✐♦♥ár✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✶✽
✶✾
✶ ■◆❚❘❖❉❯➬➹❖
❯♠❛ ♣❛r❝❡❧❛ ❝♦♠ ❣r❛♥❞❡ s✐❣♥✐✜❝â♥❝✐❛ ♥❛ ❡❝♦♥♦♠✐❛ ❜r❛s✐❧❡✐r❛ ❡stá ❞✐r❡t❛✲ ♠❡♥t❡ ❧✐❣❛❞❛ à ♣r♦❞✉çã♦ ❞❡ ❝✉❧t✉r❛s ❛❣rí❝♦❧❛s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ s♦❥❛✱ ❝❛❢é✱ ♠✐❧❤♦✱ ❛rr♦③✱ ❢❡✐❥ã♦✱ tr✐❣♦✱ ❡♥tr❡ ♦✉tr♦s✱ t❛♥t♦ ♣❛r❛ ♦ ❝♦♥s✉♠♦ ✐♥t❡r♥♦✱ q✉❛♥t♦ ♣❛r❛ ✜♥s ❞❡ ❡①♣♦rt❛çã♦✱ ❥á q✉❡ ♦ ❇r❛s✐❧ é ✉♠ ❞♦s ♣r✐♥❝✐♣❛✐s ♣r♦❞✉t♦r❡s ❡ ❡①♣♦rt❛❞♦r❡s ❞❡ss❛s ❝✉❧t✉r❛s ❡♠ ♥í✈❡❧ ♠✉♥❞✐❛❧✳
❉❡♥tr♦ ❞❡st❡ ✉♥✐✈❡rs♦ ❞♦ ❛❣r♦♥❡❣ó❝✐♦✱ t❡♠♦s ❡♠ ❡s♣❡❝✐❛❧ ❛s ❝♦♠♠♦❞✐t✐❡s ❛❣rí❝♦❧❛s✱ q✉❡ sã♦ ♣r♦❞✉t♦s ❜ás✐❝♦s q✉❡ ♣♦❞❡♠ s❡r ♣r♦❞✉③✐❞♦s ❡ ♥❡❣♦❝✐❛❞♦s ♣♦r ✉♠❛ ❛♠♣❧❛ ❣❛♠❛ ❞❡ ❡♠♣r❡s❛s✳ ■♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞♦ ♣r♦❞✉t♦r✱ ❛ q✉❛❧✐❞❛❞❡ ❞♦s ♣r♦❞✉t♦s ♥ã♦ é ❞✐❢❡r❡♥❝✐❛❞❛ ♥❡♠ s♦❢r❡ ♣r♦❝❡ss♦s ❞❡ ❛❧t❡r❛çã♦ ❡♠ ❞❡t❡r♠✐♥❛❞♦s ♣❡rí♦❞♦s ❞❡ t❡♠♣♦✳
❆ ✈❛♥t❛❣❡♠ ❞❡ ♥ã♦ ❡①✐st✐r t❛❧ ❛❧t❡r❛çã♦✱ é ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❛s ♠❡s♠❛s s❡r❡♠ ❛r♠❛③❡♥❛❞❛s ❡ ♥❡❣♦❝✐❛❞❛s ♣♦st❡r✐♦r♠❡♥t❡✱ ✐ss♦ é ❢❡✐t♦ ♣❡❧♦s ♣r♦❞✉t♦r❡s ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❡s♣❡r❛r ✉♠❛ ♠❡❧❤♦r❛ ❞❡ ♣r❡ç♦✳ ❉❡♥tr❡ ❛s ❝♦♠♠♦❞✐t✐❡s ❛❣rí❝♦❧❛s✱ ❛ s♦❥❛ ♠❡r❡❝❡ ❞❡st❛q✉❡✱ ❥á q✉❡ ♦ ❇r❛s✐❧ é ♦ ♠❛✐♦r ♣r♦❞✉t♦r ❞❡ s♦❥❛ ❞♦ ♠✉♥❞♦✱ s❡❣✉♥❞♦ ♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❆❣r✐❝✉❧t✉r❛ ❞♦s ❊st❛❞♦s ❯♥✐❞♦s✳
❖ ♣r❡ç♦ ❞❛s ❝♦♠♠♦❞✐t✐❡s ❛❣rí❝♦❧❛s ❡stá ❞✐r❡t❛♠❡♥t❡ ❧✐❣❛❞♦ ❝♦♠ ❛ ♦❢❡rt❛ ❡ ❛ ❞❡♠❛♥❞❛ ❞♦ ♠❡r❝❛❞♦✳ ❆ss✐♠ ❝♦♠♦ ♦✉tr♦s ✐♥str✉♠❡♥t♦s ✜♥❛♥❝❡✐r♦s✱ ♦ ♣r❡ç♦ ❞❛s ❝♦♠♠♦✲ ❞✐t✐❡s ❛❣rí❝♦❧❛s ♣♦ss✉❡♠ ❝♦♠♣♦rt❛♠❡♥t♦s ❞✐❢❡r❡♥❝✐❛❞♦s ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✱ ✐st♦ é✱ ❡①✐st❡♠ é♣♦❝❛s ❡♠ q✉❡ s♦❢r❡♠ ❞❡ ❣r❛♥❞❡s ✈❛r✐❛çõ❡s ❞❡ ♣r❡ç♦ ❡ ♦✉tr❛s ❡♠ q✉❡ s♦❢r❡♠ ♠❡♥♦r❡s ✈❛r✐❛çõ❡s✳ ❊st❡ ❝♦♠♣♦rt❛♠❡♥t♦ é ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ✏✈♦❧❛t✐❧✐❞❛❞❡✑✳
◆❡st❡ â♠❜✐t♦✱ ♦s ❡st✉❞♦s r❡❧❛❝✐♦♥❛❞♦s ❛ ♣r❡ç♦s ❡ à ✈♦❧❛t✐❧✐❞❛❞❡ ❞❛s ❝♦♠♠♦✲ ❞✐t✐❡s ❛❣rí❝♦❧❛s sã♦ ❢❡rr❛♠❡♥t❛s ✐♠♣♦rt❛♥t❡s ♣❛r❛ ❛ ♥❡❣♦❝✐❛çã♦ ❞❛s ♠❡s♠❛s✱ ❡ tê♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❛✉①✐❧✐❛r ♦s t♦♠❛❞♦r❡s ❞❡ ❞❡❝✐sã♦ ❛ r❡❞✉③✐r❡♠ ❛s ✐♥❝❡rt❡③❛s ♥♦ ♠♦♠❡♥t♦ ❞❡ ❛t✉❛✲ çã♦✳
P❛r❛ ❡st✉❞♦s ❞❛ ✈♦❧❛t✐❧✐❞❛❞❡✱ ♦s ♠♦❞❡❧♦s ❧✐♥❡❛r❡s ❆❘■▼❆ ✭❆✉t♦rr❡❣r❡ss✐✈♦s ■♥t❡❣r❛❞♦s ❞❡ ▼é❞✐❛s ▼ó✈❡✐s✮ ♥ã♦ sã♦ ❛❞❡q✉❛❞♦s✱ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ ♥ã♦ ❝♦♥s❡❣✉✐r❡♠ ❝❛♣t❛r ❛ ✈❛r✐â♥❝✐❛ ❝♦♥❞✐❝✐♦♥❛❧ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✳ ❙❡♥❞♦ ❛ss✐♠✱ é ♥❡❝❡ssár✐♦ ♦ ✉s♦ ❞❡ ♠♦❞❡❧♦s ♥ã♦✲❧✐♥❡❛r❡s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♦s ♠♦❞❡❧♦s ●❆❘❈❍ ✭❆✉t♦rr❡❣r❡ss✐✈♦s ●❡♥❡r❛❧✐③❛❞♦s ❝♦♠ ❍❡t❡r♦s❝❡❞❛st✐❝✐❞❛❞❡ ❈♦♥❞✐❝✐♦♥❛❧✮✳
✷✵
r❡♣r❡s❡♥t❛ ❛ ✈♦❧❛t✐❧✐❞❛❞❡✮ ❡ ❢♦r❛♠ ❛❥✉st❛❞♦s ♠♦❞❡❧♦s q✉❡ ❢♦ss❡♠ ❝❛♣❛③❡s ❞❡ ♠♦❞❡❧❛r ❡st❡ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ♠❡♠ór✐❛ ❧♦♥❣❛✿ ♦s ♠♦❞❡❧♦s ❆❘❋■▼❆ ✭❆✉t♦rr❡❣r❡ss✐✈♦s ❋r❛❝✐♦♥ár✐♦s ■♥t❡❣r❛❞♦s ❞❡ ▼é❞✐❛s ▼ó✈❡✐s✮✳
✷✶
✷ ❘❊❱■❙➹❖ ❇■❇▲■❖●❘➪❋■❈❆
✷✳✶ ❈♦♠♠♦❞✐t✐❡s ❛❣rí❝♦❧❛s
❈♦♠♠♦❞✐t✐❡s sã♦ ♣r♦❞✉t♦s ❜ás✐❝♦s✱ ❜❡♥s ❝♦♠❡r❝✐á✈❡✐s ❡ ❞❡ ❛♠♣❧♦ ❝♦♥s✉♠♦ q✉❡ ♣♦❞❡♠ s❡r ♣r♦❞✉③✐❞♦s ❡ ♥❡❣♦❝✐❛❞♦s ♣♦r ✉♠❛ ❛♠♣❧❛ ❣❛♠❛ ❞❡ ❡♠♣r❡s❛s✳ P♦❞❡♠ s❡r ♣r♦❞✉t♦s ❛❣r♦♣❡❝✉ár✐♦s✱ ❝♦♠♦ ❜♦✐ ❣♦r❞♦✱ s♦❥❛ ❡ ❝❛❢é❀ ♠✐♥❡r❛✐s✱ ❝♦♠♦ ♦✉r♦ ❡ ♣❡tró❧❡♦❀ ✐♥❞✉str✐❛✐s✱ ❝♦♠♦ t❡❝✐❞♦ ✶✵✵✪ ❛❧❣♦❞ã♦ ❡ ♣♦❧✐ést❡r❀ ❡ ❛té ♠❡s♠♦ ✜♥❛♥❝❡✐r♦s✱ ❝♦♠♦ ❛s ♠♦❡❞❛s ♠❛✐s r❡q✉✐s✐t❛❞❛s ✭❞ó❧❛r ❡ ❡✉r♦✮✱ ❛çõ❡s ❞❡ ❣r❛♥❞❡s ❡♠♣r❡s❛s✱ ❡t❝✳ ◆❡st❡ tr❛❜❛❧❤♦ s❡rá ❡♥❢❛t✐③❛❞♦ ❛♣❡♥❛s ❝♦♠♠♦❞✐t✐❡s ❛❣rí❝♦❧❛s✱ ❡♠ ♣❛rt✐❝✉❧❛r✱ ❛ s♦❥❛✳
❖ ❡st✉❞♦ ❞❡ ❝♦♠♠♦❞✐t✐❡s é ♠✉✐t♦ ✐♠♣♦rt❛♥t❡ ♥❛ ❡❝♦♥♦♠✐❛✱ ❥á q✉❡✱ ❡♠❜♦r❛ s❡❥❛♠ ♠❡r❝❛❞♦r✐❛s ♣r✐♠ár✐❛s✱ ❡①✐st❡ ✉♠ ✐♥t❡r❡ss❡ ❣❧♦❜❛❧ s♦❜r❡ ❛s ♠❡s♠❛s✳ ■st♦ ♦❝♦rr❡ ❡♠ ❜♦❧s❛s ❞❡ ♠❡r❝❛❞♦r✐❛s✱ ✐st♦ é✱ s❡✉s ♣r❡ç♦s sã♦ ❞❡✜♥✐❞♦s ❡♠ ♥í✈❡❧ ❣❧♦❜❛❧ ♣❡❧♦ ♠❡r❝❛❞♦ ✐♥t❡r♥❛❝✐♦♥❛❧ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❢❛t♦r❡s ❞❡ ♦❢❡rt❛ ❡ ❞❡♠❛♥❞❛✳ P♦r ❡st❡ ♠♦t✐✈♦ ❡stã♦ s✉❥❡✐t♦s à ♦s❝✐❧❛çõ❡s ♥❛s ❝♦t❛çõ❡s ❞❡ ♠❡r❝❛❞♦✱ ❡♠ ✈✐rt✉❞❡ ❞❡ ♣❡r❞❛s ❡ ❣❛♥❤♦s ♥♦s ✢✉①♦s ✜♥❛♥❝❡✐r♦s ♥♦ ♠✉♥❞♦✳
❯♠❛ ❝❛r❛❝t❡ríst✐❝❛ ✐♠♣♦rt❛♥t❡ s♦❜r❡ ♦s ♠❡s♠♦s✱ é q✉❡ ❜♦❛s ❝♦♠♠♦❞✐t✐❡s sã♦ ❛q✉❡❧❡s q✉❡ ❛♣r❡s❡♥t❛♠ ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ q✉❛❧✐❞❛❞❡ ✉♥✐❢♦r♠❡✱ ✐st♦ é✱ ♣♦❞❡♠ s❡r ♣r♦❞✉③✐❞♦s ❡♠ ❣r❛♥❞❡s q✉❛♥t✐❞❛❞❡s✱ ❛r♠❛③❡♥❛❞❛s ♣♦r ✉♠ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦ ❡ s♦♠❡♥t❡ ❞❡♣♦✐s✱ s❡r❡♠ ❝♦♠❡r❝✐❛❧✐③❛❞♦s✱ ✐st♦ s❡♠ ♣r❡❥✉❞✐❝❛r ❛ s✉❛ q✉❛❧✐❞❛❞❡ ✭❝♦♠♦ ❡①❡♠♣❧♦✱ s♦❥❛ ❡ ♠✐❧❤♦✮✳ ❊st❡ ❢❛t♦ é ❢❛✈♦rá✈❡❧✱ ❥á q✉❡ ♦ ♣r♦❞✉t♦r t❡♠ ❛ ♦♣çã♦ ❞❡ ✈❡♥❞❡r ♦ s❡✉ ♣r♦❞✉t♦ ♦✉ ❡st♦❝á✲❧♦ ❡ ❡s♣❡r❛r ♣♦r ✉♠❛ ♠❡❧❤♦r❛ ❞❡ ♣r❡ç♦✱ ♣♦✐s ♦ ♣r♦❞✉t♦ t❡♠ ❛ ♣r♦♣r✐❡❞❛❞❡ ❞❡ ♥ã♦ ♣❡r❡❝❡r ❡♠ ✉♠ ❝❡rt♦ t❡♠♣♦ ❞❡ ❡st♦❝❛❣❡♠ ✭❇❆❨❊❘✱ ✷✵✵✽✮✳
❖s ❝♦♥tr❛t♦s ❡ ♠❡r❝❛❞♦s ❢✉t✉r♦s ❢♦r❛♠ ♦r✐❣✐♥❛❞♦s ❞❡✈✐❞♦ à ♥❡❝❡ss✐❞❛❞❡ ❞❡ tr❛♥s❢❡r✐r ♦s r✐s❝♦s ❡♥✈♦❧✈✐❞♦s ❝♦♠ r❡❧❛çã♦ ❛♦s ♣r❡ç♦s ❞♦s ♣r♦❞✉t♦s ❛❣rí❝♦❧❛s✳ ❖ ♦❜❥❡t✐✈♦ ❞♦ ♠❡r❝❛❞♦ ❢✉t✉r♦ é ♣r♦❞✉③✐r ✉♠ ♠❡✐♦ ❞❡ ❝♦♠✉♥✐❝❛çã♦ s♦❜r❡ ♦ ♣r❡ç♦ ❞♦s ❛t✐✈♦s q✉❡ s❡rã♦ tr❛♥s❛❝✐♦♥❛❞♦s ♥♦ ❢✉t✉r♦✱ ♦ q✉❡ é ❢❡✐t♦ ❛ ✉♠ ❝✉st♦ ❜❛✐①♦ ❡ ♠✉✐t♦ ❡✜❝✐❡♥t❡✳ ❯♠ ❡①❡♠♣❧♦ ♣rát✐❝♦✱ s❡r✐❛ ✉♠ ❛❣r✐❝✉❧t♦r q✉❡ ♣r♦❞✉③ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❝✉❧t✉r❛ ❡ ♥ã♦ s❛❜❡ ♦ q✉❡ ❛❝♦♥t❡❝❡rá ❝♦♠ r❡❧❛çã♦ ❛♦s ♣r❡ç♦s ❡♠ ♦✐t♦ ♠❡s❡s✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❡①✐st❡ ♦ ❡s♣❡❝✉❧❛❞♦r q✉❡ ❞❡s❡❥❛ ❡①❛t❛♠❡♥t❡ ♦ ♦♣♦st♦ ❞♦ ❛❣r✐❝✉❧t♦r✱ ♦ ❡s♣❡❝✉❧❛❞♦r ❞❡s❡❥❛ ♦ r✐s❝♦ ✭❇❆❨❊❘✱ ✷✵✵✽✮✳
✷✷
❡①t❡♥sã♦ t❡rr✐t♦r✐❛❧ ❡ ❛♦ s✐st❡♠❛ ❛❞♦t❛❞♦✱ ✐♥❝❧✉✐♥❞♦ t♦❞❛ ❛ ❝❛❞❡✐❛ ♣r♦❞✉t✐✈❛ ❞❛s ❝✉❧t✉r❛s✱ ❝♦♠♦ ♦ ♠♦❞♦ ❞❡ ♣r♦❞✉çã♦ ❡ ❛s ❝♦♥❞✐çõ❡s ❢❛✈♦rá✈❡✐s q✉❡ ♦ ♣❛ís ❛♣r❡s❡♥t❛ ✭❛❧t❛ ❞✐✈❡rs✐❞❛❞❡ ♣r❡s❡♥t❡ ♥❛s ✈❛r✐❛❞❛s ❝♦♥❞✐çõ❡s ❝❧✐♠át✐❝❛s q✉❡ ❢❛✈♦r❡❝❡♠ ♦ ❝✉❧t✐✈♦ ❞❡ ❞✐✈❡rs♦s t✐♣♦s ❞❡ ❝✉❧t✉r❛s✮ ✭●❆❇❆◆✱ ✷✵✶✹✮✳
P❛r❛ ❛ ♥❡❣♦❝✐❛çã♦ ❞❡ ❝♦♠♠♦❞✐t✐❡s ♥♦ ❇r❛s✐❧✱ ♦s ♥❡❣ó❝✐♦s ❝♦♥❝❡♥tr❛♠✲s❡ ♥❛ ❇▼✫❋❇❖❱❊❙P❆ ✭❇♦❧s❛ ❞❡ ▼❡r❝❛❞♦r✐❛s ❡ ❋✉t✉r♦s✮✳ ❆ ❇▼✫❋❇❖❱❊❙P❆ ♦❢❡r❡❝❡ ♠✉✐t♦s ♣r♦❞✉t♦s ❡ s❡r✈✐ç♦s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✿ ♥❡❣♦❝✐❛çã♦ ❞❡ ❛çõ❡s✱ tít✉❧♦s ❞❡ r❡♥❞❛ ✜①❛✱ t❛①❛s✱ ♠❡r❝❛❞♦r✐❛s✱ ♠♦❡❞❛s✱ ❡♥tr❡ ♦✉tr♦s✳ ❆ ❇♦❧s❛ ❞á ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ s❡✉s ❝❧✐❡♥t❡s r❡❛❧✐③❛r❡♠ ♦♣❡r❛çõ❡s ❞❡st✐♥❛❞❛s à ❝♦♠♣r❛ ❡ ✈❡♥❞❛ ❞❡ ❛çõ❡s✱ tr❛♥s❢❡rê♥❝✐❛ ❞❡ r✐s❝♦s ❞❡ ♠❡r❝❛❞♦✱ ❛r❜✐tr❛❣❡♠ ❞❡ ♣r❡ç♦s ❡♥tr❡ ♠❡r❝❛❞♦s ❡✴♦✉ ❛t✐✈♦s✱ ❞✐✈❡rs✐✜❝❛çã♦ ❡ ❛❧♦❝❛çã♦ ❞❡ ✐♥✈❡st✐♠❡♥t♦s ❡ ❛❧❛✈❛♥❝❛❣❡♠ ❞❡ ♣♦s✐çõ❡s ✭❇▼✫❋❇❖❱❊❙P❆✱ ✷✵✶✹✮✳
✷✳✷ ❆ s♦❥❛ ♥♦ ❇r❛s✐❧
❆ s♦❥❛ ✐♥✐❝✐♦✉ ♦ ❝✉❧t✐✈♦ ♥♦ ❇r❛s✐❧ ❡♠ ♠❡❛❞♦s ❞❡ ✶✾✻✵ ❡♠ ♣❡q✉❡♥❛s ♣r♦♣r✐❡✲ ❞❛❞❡s ♥❛ r❡❣✐ã♦ ❙✉❧ ❞♦ ♣❛ís✿ ❛té ✶✾✼✵ ✽✵✪ ❞❛ ♣r♦❞✉t✐✈✐❞❛❞❡ ♥♦ ♣❛ís ❡r❛ ❝♦♥❝❡♥tr❛❞❛ ♥❛ r❡❣✐ã♦ ❙✉❧✳ ◆♦s ❞✐❛s ❛t✉❛✐s✱ ♦ ❝✉❧t✐✈♦ s❡ ❡st❡♥❞❡✉ ♣♦r t♦❞♦ ♦ ❈❡rr❛❞♦ ❛t✐♥❣✐♥❞♦✱ ✐♥❝❧✉s✐✈❡✱ ❛ r❡❣✐ã♦ ◆♦rt❡ ❞♦ ❇r❛s✐❧ ✭❙❈❍◆❊P❋ ❡t ❛❧✳✱ ✷✵✶✷✮✳
❆ ♣r♦❞✉t✐✈✐❞❛❞❡ ❞❡ ❝✉❧t✉r❛s ❛❣rí❝♦❧❛s t♦r♥♦✉✲s❡ ✉♠ ❣r❛♥❞❡ s✉♣♦rt❡ à ❡❝♦♥♦♠✐❛ ❜r❛s✐❧❡✐r❛✱ ❥á q✉❡ ♦ ❛❣r♦♥❡❣ó❝✐♦ é r❡s♣♦♥sá✈❡❧ ♣♦r ✉♠❛ ♣❛r❝❡❧❛ s✐❣♥✐✜❝❛t✐✈❛ ❞❛s ❡①♣♦rt❛çõ❡s ❜r❛s✐❧❡✐r❛s✳ ◆❡st❡ â♠❜✐t♦✱ ❛ ♣r♦❞✉çã♦ ❞❛ s♦❥❛ ♠❡r❡❝❡ ❞❡st❛q✉❡✱ ❥á q✉❡ é ✉♠ ❞♦s ♣r✐♥❝✐♣❛✐s ♣r♦❞✉t♦s ❡①♣♦rt❛❞♦s ♣❡❧♦ ❇r❛s✐❧✳
❆ ár❡❛ ✉t✐❧✐③❛❞❛ ♣❛r❛ ♦ ❝✉❧t✐✈♦ ❞❛ s♦❥❛ ♣❛r❛ ❛ s❛❢r❛ ✷✵✵✺✴✷✵✵✻ ❢♦✐ ❡q✉✐✈❛❧❡♥t❡ ❛ s♦♠❛ ❞❛ ár❡❛ ♣r❡✈✐st❛ ♣❛r❛ ♦s ♦✉tr♦s q✉❛tr♦ ♣r✐♥❝✐♣❛✐s ❣rã♦s ♣r♦❞✉③✐❞♦s ♥♦ ♣❛ís ✭♠✐❧❤♦✱ tr✐❣♦✱ ❛rr♦③ ❡ ❢❡✐❥ã♦✮✱ ❡ss❡s q✉❡✱ ❡♠❜♦r❛ s❡❥❛♠ ♠✉✐t♦ ❝♦♥s✉♠✐❞♦s ♣❡❧♦s ❜r❛s✐❧❡✐r♦s✱ t✐✈❡r❛♠ ✉♠❛ r❡❞✉çã♦ ♥❛ ár❡❛ ♣❧❛♥t❛❞❛ ❡♥tr❡ ♦s ❛♥♦s ❞❡ ✶✾✾✺ ❡ ✷✵✵✺✱ ❡♥q✉❛♥t♦ ❛ ár❡❛ ❞❡st✐♥❛❞❛ ❛♦ ♣❧❛♥t✐♦ ❞❡ s♦❥❛ ♦❜t❡✈❡ ♠❛✐s ❞♦ q✉❡ ♦ tr✐♣❧♦ ✭❈❆❱❆▲❊❚❚✱ ✷✵✵✽✮✳
✷✸
❊ss❛ ❛❞❛♣t❛çã♦ ❞❛ s♦❥❛ às ❝♦♥❞✐çõ❡s ❞❡ ❧❛t✐t✉❞❡s ❞❛s r❡❣✐õ❡s ❈❡♥tr♦✲❖❡st❡✱ ◆♦rt❡ ❡ ◆♦r❞❡st❡ ❢♦✐ ✉♠ ❣r❛♥❞❡ ✐♠♣❡❝í❧✐♦ ❡♥❝♦♥tr❛❞♦ ♣❡❧♦s ♣r♦❣r❛♠❛s ❞❡ ♠❡❧❤♦r❛♠❡♥t♦✱ ♣♦ré♠✱ ❝♦♠ ♦ ❛✈❛♥ç♦ ❞❛s ♣❡sq✉✐s❛s ♥❡ss❛ ár❡❛✱ t♦r♥♦✉✲s❡ ♣♦ssí✈❡❧ ❛ ❡①♣❧♦r❛çã♦ ❞❛ ♠❡s♠❛ ❡♠ r❡❣✐õ❡s ❛♥t❡s ❝♦♥s✐❞❡r❛❞❛s ✐♥❛♣t❛s ♣❛r❛ ♦ s❡✉ ❝✉❧t✐✈♦ ❡❝♦♥ô♠✐❝♦✳
❊st❡ ♣r♦❝❡ss♦ ❞❡ r❡❝♦♠❡♥❞❛çã♦ ❞❡ ❝✉❧t✐✈❛r❡s ♣❛r❛ ❛s r❡❣✐õ❡s ❞❡ ❜❛✐①❛ ❡ ♠é❞✐❛ ❧❛t✐t✉❞❡s✱ ♣♦ss✐❜✐❧✐t♦✉ q✉❡ ✈❛st❛s ár❡❛s ❞❛ r❡❣✐ã♦ tr♦♣✐❝❛❧ ❞♦s ❈❡rr❛❞♦s ✜③❡ss❡♠ ♣❛rt❡ ❞♦ ♣r♦❝❡ss♦ ♣r♦❞✉t✐✈♦ ❛❣rí❝♦❧❛ ❡ t❛♠❜é♠✱ ✈✐❛❜✐❧✐③♦✉ ❛ ❡①♣❧♦r❛çã♦ ❞❡ ♦✉tr❛s ❡s♣é❝✐❡s ❞❡ ❝✉❧t✉r❛s ✭❆▲▼❊■❉❆ ❡t ❛❧✳✱ ✶✾✾✾✮✳
✷✳✸ ❊st✉❞♦s r❡❧❛❝✐♦♥❛❞♦s à ✈♦❧❛t✐❧✐❞❛❞❡ ❞❛ s♦❥❛
❆ ✈♦❧❛t✐❧✐❞❛❞❡ ❞❛s ❝♦♠♠♦❞✐t✐❡s ❛❣rí❝♦❧❛s✱ ❡♠ ♣❛rt✐❝✉❧❛r ❞❛ s♦❥❛✱ ✈❡♠ s❡♥❞♦ ❝❛❞❛ ✈❡③ ♠❛✐s ❡st✉❞❛❞❛ ❛♦ ❧♦♥❣♦ ❞♦s ❛♥♦s ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❡①♣❧✐❝❛r ❝❛❞❛ ✈❡③ ♠❡❧❤♦r ♦ s❡✉ ❝♦♠♣♦rt❛♠❡♥t♦✳
❈♦♠ ❡st❡ ♦❜❥❡t✐✈♦✱ ❛❧❣✉♥s t✐♣♦s ❞❡ ❞❛❞♦s ❥á ❢♦r❛♠ ✉t✐❧✐③❛❞♦s✱ ❞❡s❞❡ ❞❛❞♦s ❞❡ ❛❧t❛ ❢r❡q✉ê♥❝✐❛ ✉t✐❧✐③❛❞♦s ♣♦r ❙✐♠õ❡s ❡t✳ ❛❧ ✭✷✵✶✷✮ ♦✉ ♠❛✐s ❝♦♠✉♠❡♥t❡ ❞❛❞♦s ❞✐ár✐♦s✳ ❚❛♠❜é♠✱ ❤á tr❛❜❛❧❤♦s q✉❡ ❡st✉❞❛♠ ❛ sér✐❡ ❞❡ ♠❛♥❡✐r❛ ❞✐r❡t❛ ❝♦♠♦ ❡♠ ❇❛②❡r ✭✷✵✵✽✮✱ ❡♠ q✉❡ ♦ ❛❥✉st❡ ❞♦ ♠♦❞❡❧♦ é ❢❡✐t♦ ❞✐r❡t❛♠❡♥t❡ ♥❛ sér✐❡ ❞❡ ♣r❡ç♦s✱ ❝♦♥tr❛st❛♥❞♦ ❝♦♠ ❛ ♠❛✐♦r✐❛ ❞♦s tr❛❜❛❧❤♦s ❡♥❝♦♥tr❛❞♦s✱ ❡♠ q✉❡ ♦s ♠♦❞❡❧♦s sã♦ ❛❥✉st❛❞♦s ♥❛ sér✐❡s ❞❡ r❡t♦r♥♦s ❞♦s ♣r❡ç♦s✳
❆ ❛❜♦r❞❛❣❡♠ ♠❛✐s ❝♦♠✉♠ ♥♦ â♠❜✐t♦ ❛❝❛❞ê♠✐❝♦ q✉❡ ❝♦♥t❡♠♣❧❛ ❛ ✈♦❧❛t✐❧✐✲ ❞❛❞❡✱ é ❛ ✉t✐❧✐③❛çã♦ ❞❡ ♠♦❞❡❧♦s ❞❛ ❢❛♠í❧✐❛ ●❆❘❈❍ ❝♦♠♦ ❡♠ ❈❛♠♣♦s ✫ ❈❛♠♣♦s ✭✷✵✵✼✮ ❡ ▲✐♠❛ ❡t✳ ❛❧ ✭✷✵✵✼✮✱ q✉❡ ♦❜s❡r✈❛r❛♠ ✉♠ ❝❛rát❡r ♣❡rs✐st❡♥t❡ ❞❛ ✈♦❧❛t✐❧✐❞❛❞❡ ❞♦s ❞❛❞♦s✱ ❡♥q✉❛♥t♦ ❙✐❧✈❛ ✫ ▼❛✐❛ ✭✷✵✶✷✮ ♦❜s❡r✈❛r❛♠ ✉♠❛ ❞❡♣❡♥❞ê♥❝✐❛ ❞❡ ❝✉rt❛ ❞✉r❛çã♦✱ ❥á q✉❡ ♦❜✲ t❡✈❡ ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ♣❛r❛ ❛ ♣r❡✈✐sã♦ ❞❛ ✈♦❧❛t✐❧✐❞❛❞❡ ❝♦♠ ♦s ♠♦❞❡❧♦s ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ❝♦♠ ❥❛♥❡❧❛ ♠ó✈❡❧ ❞❡ ✶✵ ❞✐❛s✳
✷✹
✷✳✹ ❙ér✐❡s t❡♠♣♦r❛✐s
❊①✐st❡♠ ♠✉✐t♦s ❢❡♥ô♠❡♥♦s ♥❛t✉r❛✐s✱ ❡❝♦♥ô♠✐❝♦s✱ ❞❡♥tr❡ ♦✉tr♦s✱ ❝✉❥❛s ♦❜s❡r✈❛çõ❡s ❢♦r♠❛♠ ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❞❛❞♦s ❞✐str✐❜✉í❞♦s ♥♦ t❡♠♣♦✳ ❊st❛ s❡q✉ê♥❝✐❛ ❞❡ ❞❛❞♦s ♦r❞❡♥❛❞♦s s♦❜r❡ ♦ ♣❛râ♠❡tr♦ t❡♠♣♦ é ❞❡♥♦♠✐♥❛❞❛ ✏sér✐❡ t❡♠♣♦r❛❧✑ ✭❙❖❯❩❆✱ ✶✾✽✶✮✳
❖ ❡st✉❞♦ ❞❡ ❛♥á❧✐s❡ ❡ ♣r❡✈✐sã♦ ❞❡ sér✐❡s t❡♠♣♦r❛✐s t❡♠ r❡❝❡❜✐❞♦ ✉♠❛ ❛t❡♥çã♦ ❡s♣❡❝✐❛❧ ♥❛s ú❧t✐♠❛s ❞é❝❛❞❛s✳ ▼✉✐t♦s ♠ét♦❞♦s ❡st❛tíst✐❝♦s tê♠ s✐❞♦ ❞❡s❡♥✈♦❧✈✐❞♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞❡ ♣r❡✈✐sõ❡s ❝❛❞❛ ✈❡③ ♠❛✐s ♣r❡❝✐s❛s ❡♠ sér✐❡s t❡♠♣♦r❛✐s ♠❛❝r♦❡❝♦♥ô♠✐❝❛s✱ ❡♠ sér✐❡s ❞❡ ❝♦♥s✉♠♦ ♦✉ ❡♠ ♦✉tr❛s ár❡❛s ❞❡ ♣❡sq✉✐s❛ ✭❇❆❨❊❘❀ ❙❖❯❩❆✱ ✷✵✶✵✮✳
❆ ❛♥á❧✐s❡ ❞❡ sér✐❡s t❡♠♣♦r❛✐s t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❜✉s❝❛r ❛❧❣✉♠❛ r❡❧❛çã♦ ❞❡ ❞❡♣❡♥❞ê♥❝✐❛ t❡♠♣♦r❛❧ s♦❜r❡ ♦s ❞❛❞♦s✱ ✐❞❡♥t✐✜❝❛♥❞♦ ♦ ♠❡❝❛♥✐s♠♦ ❣❡r❛❞♦r ❞❛ sér✐❡✱ ❡①tr❛✐♥❞♦✲s❡ ♣❡r✐♦❝✐❞❛❞❡s q✉❡ s❡❥❛♠ r❡❧❡✈❛♥t❡s ♥❛s ♦❜s❡r✈❛çõ❡s✱ ❞❡s❝r❡✈❡r ♦ s❡✉ ❝♦♠♣♦r✲ t❛♠❡♥t♦ ❡ r❡❛❧✐③❛r ♣r❡✈✐sõ❡s✳
▼♦❞❡❧♦s ❞❡ sér✐❡s t❡♠♣♦r❛✐s ♣♦❞❡♠ s❡r ❛♣❧✐❝❛❞♦s ♥❛s ♠❛✐s ❞✐✈❡rs❛s ár❡❛s✱ ♠❛s ♥♦ â♠❜✐t♦ ✜♥❛♥❝❡✐r♦ ❡①✐st❡ ✉♠❛ ♣❡❝✉❧✐❛r✐❞❛❞❡✿ ❡♠ ❣❡r❛❧✱ sér✐❡s q✉❡ ♣r♦✈ê♠ ❞❡ ❞❛❞♦s ✜♥❛♥❝❡✐r♦s ❛♣r❡s❡♥t❛♠ ✈❛r✐❡❞❛❞❡ ❛ q✉❛❧ ❢♦✐ ❞❡♥♦♠✐♥❛❞❛ ✏✈♦❧❛t✐❧✐❞❛❞❡✑✱ ❡st❛ q✉❡ ♥ã♦ é ❞✐r❡t❛♠❡♥t❡ ♦❜s❡r✈á✈❡❧✳ P❛r❛ ❧❡✈❛r ❛ ✈♦❧❛t✐❧✐❞❛❞❡ ❡♠ ❝♦♥s✐❞❡r❛çã♦✱ ❢❛③✲s❡ ♥❡❝❡ssár✐♦ r❡❝♦rr❡r ❛ ♠♦❞❡❧♦s ❤❡t❡r♦s❝❡❞ást✐❝♦s ❝♦♥❞✐❝✐♦♥❛✐s✱ ❥á q✉❡ ❛ ✈♦❧❛t✐❧✐❞❛❞❡ ♥❛❞❛ ♠❛✐s é q✉❡ ✉♠❛ ✈❛r✐â♥❝✐❛ ♥ã♦ ❝♦♥st❛♥t❡✱ ✐st♦ é✱ ✉♠❛ ✈❛r✐â♥❝✐❛ ❞❡♣❡♥❞❡♥t❡ ❞♦ ✐♥st❛♥t❡ ❞❡ t❡♠♣♦ ♥♦ q✉❛❧ s❡ ❡♥❝♦♥tr❛ ✭❇❆❨❊❘✱ ✷✵✵✽✮✳
❙❡❣✉♥❞♦ ❍❛r❞✐❡ ❡t ❛❧✳ ✭✶✾✾✽✮✱ ❝♦♠ ♦ ❛✈❛♥ç♦ ❞♦s r❡❝✉rs♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❢♦✐ ♣♦ssí✈❡❧ ❛✉♠❡♥t❛r ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❡ ❞❡ ❛r♠❛③❡♥❛♠❡♥t♦✱ ❢❛t♦ q✉❡ ✐♥❝❡♥t✐✈♦✉ ♦s ♣❡sq✉✐s❛❞♦r❡s ❛ ❞❡s❡♥✈♦❧✈❡r❡♠ té❝♥✐❝❛s ❞❡ ♣r❡✈✐sã♦ ❡ tr❛❜❛❧❤❛r ❝♦♠ ❛♥á❧✐s❡s q✉❛❧✐t❛t✐✈❛s ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ♦❜t❡r ✉♠❛ ♠❡❧❤♦r ♣r❡❝✐sã♦✳
✷✳✺ ❊st❛❝✐♦♥❛r✐❡❞❛❞❡
❯♠❛ s✉♣♦s✐çã♦ ❢❡✐t❛ ❝♦♠ ❢r❡q✉ê♥❝✐❛ ❡♠ ✉♠❛ sér✐❡ t❡♠♣♦r❛❧✱ é q✉❡ ❛ ♠❡s♠❛ s❡❥❛ ❡st❛❝✐♦♥ár✐❛✱ ✐st♦ é✱ q✉❡ ❡❧❛ s❡ ❞❡s❡♥✈♦❧✈❛ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ ❛❧❡❛t♦r✐❛♠❡♥t❡ ❡♠ t♦r♥♦ ❞❡ ✉♠❛ ♠é❞✐❛ ❝♦♥st❛♥t❡✱ ❡st❛♥❞♦ ❞❡st❡ ♠♦❞♦✱ ❡♠ ❡q✉✐❧í❜r✐♦ ❡stá✈❡❧✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ♥❛ ♣rát✐❝❛✱ ❛ ♠❛✐♦r✐❛ ❞❛s sér✐❡s sã♦ ♥ã♦✲❡st❛❝✐♦♥ár✐❛s✳
✷✺
✭▼❖❘❊❚❚■◆❀ ❚❖▲❖■✱ ✷✵✵✹✮✳
✷✳✻ ❋❛♠í❧✐❛ ❆❘■▼❆
❆ ❝❧❛ss❡ ❞❡ ♠♦❞❡❧♦s ❆❘■▼❆ ✭❆✉t♦rr❡❣r❡ss✐✈♦s ■♥t❡❣r❛❞♦s ❞❡ ▼é❞✐❛s ▼ó✈❡✐s✮ é ❛ ♠❛✐s ✉t✐❧✐③❛❞❛ ❡♠ ❛♥á❧✐s❡ ❞❡ sér✐❡s t❡♠♣♦r❛✐s✱ ♣r♦♣♦st♦s ♣♦r ❇♦① ✫ ❏❡♥❦✐♥s ✭✶✾✼✵✮❀ ♣♦r ❡ss❡ ♠♦t✐✈♦✱ t❛♠❜é♠ sã♦ ❝♦♥❤❡❝✐❞♦s ♥❛ ❧✐t❡r❛t✉r❛ ❝♦♠♦ ♠♦❞❡❧♦s ❇♦① ✫ ❏❡♥❦✐♥s✳
❆ ♥♦t❛çã♦ ✉t✐❧✐③❛❞❛ é ❆❘■▼❆✭p, d, q✮✱ ❡♠ q✉❡ p é ♦ ♥ú♠❡r♦ ❞❡ ♣❛râ♠❡tr♦s
❞❛ ♣❛rt❡ ❛✉t♦rr❡❣r❡ss✐✈❛ ✭❆❘✮✱dé ♦ ♥ú♠❡r♦ ❞❡ ❞✐❢❡r❡♥ç❛s ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛ sér✐❡ s❡ t♦r♥❛r
❡st❛❝✐♦♥ár✐❛ ❡ q é ♦ ♥ú♠❡r♦ ❞❡ ♣❛râ♠❡tr♦s ❞❛ ♣❛rt❡ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✭▼❆✮✳ P❛r❛ ❡st❡s
t✐♣♦s ❞❡ ♠♦❞❡❧♦s✱ ❛ss✉♠❡✲s❡ q✉❡ p, d, q ∈Z+ ✭❇❆❨❊❘✱ ✷✵✵✽✮✳
❖ ♠♦❞❡❧♦ ❆❘■▼❆ ♣♦❞❡ s❡r ✐❞❡♥t✐✜❝❛❞♦ ❝♦♠♦ ✉♠ t♦❞♦ ♥♦ ♠♦❞❡❧♦ ♦✉ ♣❛r❝✐❛❧♠❡♥t❡✱ ♦✉ s❡❥❛✱ ♣♦❞❡✲s❡ ✐❞❡♥t✐✜❝❛r ♠♦❞❡❧♦s ❆❘✭p✮ ✭❛♣❡♥❛s ❛ ♣❛rt❡ ❛✉t♦rr❡❣r❡ss✐✈❛
é ✐♠♣♦rt❛♥t❡ ♣❛r❛ ♠♦❞❡❧❛r ❛ sér✐❡ ❡♠ q✉❡stã♦✮ ♦✉ ♠♦❞❡❧♦s ▼❆✭q✮ ✭❛♣❡♥❛s ❛ ♣❛rt❡ ❞❡
♠é❞✐❛s ♠ó✈❡✐s é ✐♥t❡r❡ss❛♥t❡ ♣❛r❛ ♦ ♠♦❞❡❧❛r ❛ sér✐❡✮✳ ◆❡st❡ â♠❜✐t♦✱ t❡♠✲s❡ ♦s ♠♦❞❡❧♦s ♠✐st♦s ❝♦♠♣♦st♦s ♣❡❧❛ ♣❛rt❡ ❛✉t♦rr❡❣r❡ss✐✈❛ ❡ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s✱ ❝♦♠ ♦✉ s❡♠ ❞✐❢❡r❡♥❝✐❛çã♦✳
✷✳✻✳✶ ▼♦❞❡❧♦ ❛✉t♦rr❡❣r❡ss✐✈♦ ✲ ❆❘
❖ ♠♦❞❡❧♦ ❛✉t♦rr❡❣r❡ss✐✈♦ ✲ ❆❘ é ✉t✐❧✐③❛❞♦ q✉❛♥❞♦ ❛♣❡♥❛s ❛s ♦❜s❡r✈❛çõ❡s ♣❛ss❛❞❛s sã♦ r❡❧❡✈❛♥t❡s ♣❛r❛ ❡①♣❧✐❝❛r ❛ sér✐❡ ❡♠ q✉❡stã♦✱ ✐st♦ é✱ q✉❛♥❞♦ ❡①✐st❡ ❛✉t♦❝♦r✲ r❡❧❛çã♦ ❡♥tr❡ ❛s ♦❜s❡r✈❛çõ❡s✳ ❙❡❣✉♥❞♦ ▼❛❦r✐❞❛❦✐s ❡t ❛❧✳ ✭✶✾✽✸✮✱ ♦s ♠♦❞❡❧♦s ❆❘ ♠❛✐s ❝♦♠✉♥s ♥❛s ♣❡sq✉✐s❛s ❛❝❛❞ê♠✐❝❛s sã♦ ♦s ❞❡ ♦r❞❡♠ ✶ ❡ ✷ ✭♠♦❞❡❧♦s ♣❛r❝✐♠♦♥✐♦s♦s✮✳
❈❛s♦ ♦s ✈❛❧♦r❡s ❞❛ sér✐❡ ♣♦ss❛♠ s❡r r❡♣r❡s❡♥t❛❞♦s ♥❛ ❢♦r♠❛ ❞♦s ♠♦❞❡❧♦s ❆❘✱ ❞❡♣♦✐s ❞❛ ❡str✉t✉r❛ ❞♦ ♣r♦❝❡ss♦ ❣❡r❛❞♦r ❞❛ sér✐❡ s❡r ✐❞❡♥t✐✜❝❛❞❛ ❡ ❛♣ós ♦s ♣❛râ♠❡tr♦s s❡r❡♠ ❡st✐♠❛❞♦s✱ ♦ ♠♦❞❡❧♦ s❡rá ✉t✐❧✐③❛❞♦ ♣❛r❛ ♣r❡✈✐sã♦ ❞❡ ✈❛❧♦r❡s ❢✉t✉r♦s ❞❛ sér✐❡ ❡♠ q✉❡stã♦ ✭❙❖❯❩❆✱ ✷✵✵✻✮✳
✷✳✻✳✷ ▼♦❞❡❧♦ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✲ ▼❆
❊st❡ ♠♦❞❡❧♦ ❝♦♥s✐st❡ ❡♠ ❝❛❧❝✉❧❛r ❛ ♠é❞✐❛ ❞❛s ú❧t✐♠❛s n ♦❜s❡r✈❛çõ❡s ♠❛✐s
✷✻
♣❡rí♦❞♦ ✭▼❆❑❘■❉❆❑■❙ ❡t ❛❧✳✱ ✶✾✾✽✮✳
❉❡ ♠❛♥❡✐r❛ ❣❡r❛❧✱ ❡st❡ ♠♦❞❡❧♦ ✉t✐❧✐③❛ ❞❛❞♦s ❡st✐♠❛❞♦s ❛♥t❡r✐♦r♠❡♥t❡ ❞❡ ✉♠ ♥ú♠❡r♦ q ❞❡ ♣❡rí♦❞♦s ✭❞❡t❡r♠✐♥❛❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❣❡r❛❧♠❡♥t❡ ♦s ♣❡rí♦❞♦s ♠❛✐s r❡❝❡♥t❡s✮
♣❛r❛ ❣❡r❛r ❛ ♣r❡✈✐sã♦✳ ❆ ❝❛❞❛ ♥♦✈♦ ♣❡rí♦❞♦ ❞❡ ♣r❡✈✐sã♦✱ ♦s ❞❛❞♦s ♠❛✐s ❛♥t✐❣♦s sã♦ s✉❜st✐t✉í❞♦s ♣❡❧♦s ♠❛✐s r❡❝❡♥t❡s✳ P♦r ❡st❡ ♠♦t✐✈♦✱ ♦ ♠♦❞❡❧♦ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s t❛♠❜é♠ é r❡♣r❡s❡♥t❛❞♦ ♣♦r ▼❆(q)✳
P❛r❛ ✉t✐❧✐③❛r ♦ ♠♦❞❡❧♦ ▼❆✭q✮ ♥ã♦ ❡①✐st❡ ✉♠❛ r❡❣r❛ s♦❜r❡ ♦ ♣❡rí♦❞♦ ❛
s❡r ❝♦♥s✐❞❡r❛❞♦ s♦❜r❡ ♦ ♠❡s♠♦✱ s❡♥❞♦ ❛ss✐♠✱ ❝❛❜❡rá ❛♦ ♣❡sq✉✐s❛❞♦r ❜✉s❝❛r ❛ ♠❡❧❤♦r ❛♠♣❧✐t✉❞❡ ❛ s❡ ❝♦♥s✐❞❡r❛r s❛❜❡♥❞♦ q✉❡✱ q✉❛♥t♦ ♠❛✐♦r ♦ ♣❡rí♦❞♦✱ ♠❛✐s s✉❛✈❡ s❡rá ♦ ❝♦♠✲ ♣♦rt❛♠❡♥t♦ ❞❛ ♠é❞✐❛✳ P♦r ♦✉tr♦ ❧❛❞♦✱ s❡ ♦ ♣❡rí♦❞♦ ❢♦r ♠✉✐t♦ ❛♠♣❧♦✱ ♣♦❞❡rá r❡s♣♦♥❞❡r ❧❡♥t❛♠❡♥t❡ às ♠✉❞❛♥ç❛s ❝♦♥s✐❞❡r❛❞❛s s✐❣♥✐✜❝❛t✐✈❛s ♥♦ ♠❡r❝❛❞♦✳
❯♠ ❢❛t♦r ♥❡❣❛t✐✈♦ ❧✐❣❛❞♦ ❛ ❡st❡ ♠♦❞❡❧♦✱ é ♦ ❢❛t♦ ❞❡ q✉❡ ❡❧❡ s❡ r❡❧❛❝✐♦♥❛ ❝♦♠ ❛ ❡s❝♦❧❤❛ ❞❡ ♣❡rí♦❞♦s ✉t✐❧✐③❛❞♦s ♥❛ ♣r❡✈✐sã♦✱ ✐st♦ é✱ ♦ ♥ú♠❡r♦ ❞❡ ♣❡rí♦❞♦s ✉t✐❧✐③❛❞♦s ♥♦ ❝á❧❝✉❧♦ ❞❛ ♠é❞✐❛ ♠ó✈❡❧ ❞❡t❡r♠✐♥❛ s✉❛ s❡♥s✐❜✐❧✐❞❛❞❡ ❝♦♠ r❡❧❛çã♦ ❛♦s ❞❛❞♦s ♠❛✐s r❡❝❡♥t❡s ✭❈❆❘❉❖❙❖✱ ✷✵✵✺✮✳
✷✳✻✳✸ ▼♦❞❡❧♦ ❛✉t♦rr❡❣r❡ss✐✈♦ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✲ ❆❘▼❆
◆❛ ♣rát✐❝❛✱ ♠✉✐t❛s sér✐❡s t❡♠♣♦r❛✐s ❛♣r❡s❡♥t❛♠ ❛✉t♦❝♦rr❡❧❛çã♦ ❝♦♠ ✉♠ ❝♦♠✲ ♣♦rt❛♠❡♥t♦ ♠❛✐s ❝♦♠♣❧❡①♦ ❞♦ q✉❡ ❛♣❡♥❛s ❛✉t♦rr❡❣r❡ss✐✈♦ ♦✉ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s✳ ◗✉❛♥❞♦ ✐st♦ ❛❝♦♥t❡❝❡✱ ❡①✐st❡ ❞✐✜❝✉❧❞❛❞❡ ❡♠ ❛❥✉st❛r ♠♦❞❡❧♦s✱ ♦ q✉❡ ❛❝❛rr❡t❛ ❛ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ♠✉✐t♦s ♣❛râ♠❡tr♦s ♣❛r❛ q✉❡ ❛ sér✐❡ s❡ t♦r♥❡ ✉♠ r✉í❞♦ ❜r❛♥❝♦✳
P❛r❛ s❛♥❛r ❡st❡ t✐♣♦ ❞❡ ❞✐✜❝✉❧❞❛❞❡✱ r❡❝♦♠❡♥❞❛✲s❡ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ♠♦❞❡❧♦s q✉❡ ❝♦♠❜✐♥❡♠ ♣❛râ♠❡tr♦s ❛✉t♦rr❡❣r❡ss✐✈♦s ❝♦♠ ♦s ❞❡ ♠é❞✐❛s ♠ó✈❡✐s✱ ♦ q✉❡ r❡s✉❧t❛ ♥♦s ♠♦❞❡❧♦s ❛✉t♦rr❡❣r❡ss✐✈♦s ❡ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✲ ❆❘▼❆ ✭▲❊▼❖❙✱ ✷✵✶✹✮✳
❙❡❣✉♥❞♦ ❇♦① ✫ ❏❡♥❦✐♥s ✭✶✾✼✵✮✱ ✉♠ ♣r♦❝❡ss♦ ❡st♦❝ást✐❝♦ ❡st❛❝✐♦♥ár✐♦ ♣♦❞❡ s❡r r❡♣r❡s❡♥t❛❞♦ ❞❡ ♠❛♥❡✐r❛ s❛t✐s❢❛tór✐❛ ♣♦r ✉♠ ♠♦❞❡❧♦ ❆❘▼❆ ♣❡❧♦ ❢❛t♦ ❞❡ ♣♦ss✉✐r ♠é❞✐❛✱ ✈❛r✐â♥❝✐❛ ❡ ❛✉t♦❝♦rr❡❧❛çã♦ ✐♥✈❛r✐❛♥t❡s ♥♦ t❡♠♣♦✱ ♦❜t✐❞♦ ♣❡❧❛ ♣❛ss❛❣❡♠ ❞❡ ✉♠❛ sér✐❡ r✉í❞♦ ❜r❛♥❝♦ ♣♦r ✉♠ ✜❧tr♦ ❧✐♥❡❛r✱ ♦ q✉❡ s✐❣♥✐✜❝❛ q✉❡ ❛ sér✐❡ r❡s✉❧t❛♥t❡ ♣♦❞❡rá s❡r ✈✐st❛ ❝♦♠♦ ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❧✐♥❡❛r ❞♦s t❡r♠♦s ❞❛ sér✐❡ ♦r✐❣✐♥❛❧ ✭❘■❇❊■❘❖❀ P❆❯▲❆✱ ✷✵✵✵✮✳
✷✼
❞❡❝♦rr❡r ❞♦ t❡♠♣♦ ✭❍❆❚❆❉❆◆■✱ ✷✵✵✹✮✳
✷✳✻✳✹ ▼♦❞❡❧♦ ❛✉t♦rr❡❣r❡ss✐✈♦ ✐♥t❡❣r❛❞♦ ❡ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✲ ❆❘■▼❆
❊♠ ❛♥á❧✐s❡ ❞❡ sér✐❡s t❡♠♣♦r❛✐s✱ é s❡♠♣r❡ ✈✐á✈❡❧ q✉❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♦❜✲ s❡r✈❛çõ❡s s❡❥❛♠ ❡stá✈❡✐s ♥♦ ❞❡❝♦rr❡r ❞♦ t❡♠♣♦✱ ❣❛r❛♥t✐♥❞♦ ❛ss✐♠✱ ❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡ ✉♠ ♣r♦❝❡ss♦ ❡st❛❝✐♦♥ár✐♦✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ♥❛ ♠❛✐♦r ♣❛rt❡ ❞❛s ✈❡③❡s✱ ❛s sér✐❡s ❞✐✜❝✐❧♠❡♥t❡ ❛♣r❡s❡♥t❛♠ ❡st❛❝✐♦♥❛r✐❡❞❛❞❡✱ ❢❛③❡♥❞♦✲s❡ ♥❡❝❡ssár✐❛s tr❛♥s❢♦r♠❛çõ❡s q✉❡ ❞❡✐①❡♠ ❛ sér✐❡ ❡s✲ t❛❝✐♦♥ár✐❛✳
❖ ♣r♦❝❡❞✐♠❡♥t♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❢❛③❡r t❛❧ tr❛♥s❢♦r♠❛çã♦ é ❞❡♥♦♠✐♥❛❞♦ ✏❞✐✲ ❢❡r❡♥❝✐❛çã♦✑❀ q✉❛♥❞♦ t♦♠❛♠✲s❡ ❞✐❢❡r❡♥ç❛s ♣❛r❛ ❡st❡ ♠❡s♠♦ ♣r♦♣ós✐t♦ s♦❜r❡ ❛ sér✐❡✱ ♦ ♣r♦❝❡ss♦ ❞❡♥♦♠✐♥❛✲s❡ ✏✐♥t❡❣r❛çã♦✑ ✭r❡♣r❡s❡♥t❛❞♦ ♣❡❧❛ ❧❡tr❛ ■ ❞♦ ❛❧❢❛❜❡t♦✮✳ ❉❡st❡ ♠♦❞♦✱ ♦ ♠♦❞❡❧♦ ❆❘▼❆ ♣❛ss❛ ❛ s❡r ❞❡♥♦♠✐♥❛❞♦ ♠♦❞❡❧♦ ❆❘■▼❆ ✭❇❆❨❊❘✱ ✷✵✵✽✮✳ ❖ ♠♦❞❡❧♦ ❆❘■▼❆ ❡♥❣❧♦❜❛ ❝❛❞❛ ✉♠ ❞♦s ♠♦❞❡❧♦s ❧✐st❛❞♦s ❛❜❛✐①♦ ✭❈❆❘❉❖❙❖✱ ✷✵✵✺✮✿
• ❖ ♠♦❞❡❧♦ ❛✉t♦rr❡❣r❡ss✐✈♦ ❞❡ ♦r❞❡♠ p✿ ❆❘✭p✮✱ q✉❡ é ✉t✐❧✐③❛❞♦ q✉❛♥❞♦ ❡①✐st❡ ❛✉t♦✲
❝♦rr❡❧❛çã♦ ❡♥tr❡ ❛s ♦❜s❡r✈❛çõ❡s❀
• ❖ ♠♦❞❡❧♦ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ❞❡ ♦r❞❡♠ q✿ ▼❆✭q✮✱ q✉❡ é ✉t✐❧✐③❛❞♦ q✉❛♥❞♦ ❡①✐st❡
❛✉t♦❝♦rr❡❧❛çã♦ ❡♥tr❡ ♦s r❡sí❞✉♦s❀
• ❖ ♠♦❞❡❧♦ ❛✉t♦rr❡❣r❡ss✐✈♦ ❡ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s✿ ❆❘▼❆✭p, q✮✱ q✉❡ é ✉t✐❧✐③❛❞♦ q✉❛♥❞♦
❡①✐st❡ ❛✉t♦❝♦rr❡❧❛çã♦ ❡♥tr❡ ❛s ♦❜s❡r✈❛çõ❡s ❡ ❛✉t♦❝♦rr❡❧❛çã♦ ❡♥tr❡ ♦s r❡sí❞✉♦s s✐♠✉❧✲ t❛♥❡❛♠❡♥t❡❀
• ❖ ♠♦❞❡❧♦ ❛✉t♦rr❡❣r❡ss✐✈♦ ✐♥t❡❣r❛❞♦ ❡ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s✿ ❆❘■▼❆✭p, d, q✮✱ q✉❡ é ✉t✐✲
❧✐③❛❞♦ ❡♠ sér✐❡s ♥ã♦✲❡st❛❝✐♦♥ár✐❛s✱ ✐st♦ é✱ sér✐❡s q✉❡ ♥ã♦ ♣♦ss✉❡♠ ♠é❞✐❛ ❝♦♥st❛♥t❡ ♥♦ ♣❡rí♦❞♦ ❞❡ ❛♥á❧✐s❡✳
❖ ♠♦❞❡❧♦ ❆❘■▼❆ ♣♦❞❡ ♣♦ss✉✐r t❡r♠♦s ❛✉t♦rr❡❣r❡ss✐✈♦s ❡ ♣♦❞❡♠ s❡r ✐♥t❡✲ ❣r❛❞♦s q✉❛♥❞♦ ♦s ❞❛❞♦s ♦r✐❣✐♥❛✐s ♥ã♦ sã♦ ❡st❛❝✐♦♥ár✐♦s✱ ❞❡st❡ ♠♦❞♦✱ ❢❛r✲s❡✲á ♥❡❝❡ssár✐♦ ❞✐❢❡r❡♥❝✐❛r ❛ sér✐❡ ✐♥✐❝✐❛❧ ❞❡ ❞❛❞♦sd✈❡③❡s ❛té s❡ ♦❜t❡r ✉♠❛ sér✐❡ ❡st❛❝✐♦♥ár✐❛ ✭s✉❛ ♠é❞✐❛ ❡
✈❛r✐â♥❝✐❛ ❞❡✈❡rã♦ s❡r ❝♦♥st❛♥t❡s ♥♦ t❡♠♣♦✮✳ ❆♣ós ✐st♦ s❡r ❢❡✐t♦✱ ❛ sér✐❡ ♦❜t✐❞❛ ♣♦❞❡rá s❡r ♠♦❞❡❧❛❞❛ ♣♦r ✉♠ ♠♦❞❡❧♦ ❆❘▼❆ ✭p, q✮ ✭❙❚❊◆●❊▲✱ ✶✾✽✻✮✳ ❖ ♠♦❞❡❧♦ ❆❘■▼❆ ❞❡s❝r❡✈❡
sér✐❡s ❡♠ q✉❡ ❛s ❝♦rr❡❧❛çõ❡s ♣♦ss✉❡♠ ❞❡❝❛✐♠❡♥t♦ ❧❡♥t♦ ✭❍❆❚❆❉❆◆■✱ ✷✵✵✹✮✳
✷✽
✉t✐❧✐③❛r té❝♥✐❝❛s ❡♠ q✉❡ ❛ ❡str✉t✉r❛ r❡s✐❞✉❛❧ s❡❥❛ ✉♠ r✉í❞♦ ❜r❛♥❝♦✱ ♦✉ s❡❥❛✱ q✉❡ ♦ r❡sí❞✉♦ s❡❥❛ ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ i.i.d.✳
❙❡❣✉♥❞♦ ❈❛r❞♦s♦ ✭✷✵✵✺✮✱ ♦ ♠ét♦❞♦ ❞❡ ♣r❡✈✐sã♦ ♣♦r ♠❡✐♦ ❞♦s ♠♦❞❡❧♦s ❆❘■▼❆ é s✉❜❞✐✈✐❞✐❞♦ ❡♠ q✉❛tr♦ ❡t❛♣❛s✿
✶✳ ■❞❡♥t✐✜❝❛çã♦✿ ❊♥❝♦♥tr❛r ♦s ✈❛❧♦r❡s ❞❡p✱d❡qq✉❡ s❡❥❛♠ ❛♣r♦♣r✐❛❞♦s ♣❛r❛ ❞❡s❝r❡✈❡r
♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ sér✐❡❀
✷✳ ❊st✐♠❛çã♦✿ ❆♣ós t❡r♠✐♥❛r ❛ ❡t❛♣❛ ❛♥t❡r✐♦r✱ ❞❡✈❡✲s❡ ❡st✐♠❛r ♦s ♣❛râ♠❡tr♦s ❛✉t♦r✲ r❡❣r❡ss✐✈♦s ❡ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✐♥❝❧✉í❞♦s ♥♦ ♠♦❞❡❧♦ ✭♣♦❞❡ s❡r r❡❛❧✐③❛❞♦ ♣❡❧♦ ♠ét♦❞♦ ❞♦s ♠í♥✐♠♦s q✉❛❞r❛❞♦s✮❀
✸✳ ❉✐❛❣♥óst✐❝♦✿ ❆♣ós ❞❡t❡r♠✐♥❛r ✉♠ ♠♦❞❡❧♦ ❆❘▼❆ ❡ ❡st✐♠❛r ♦s ♣❛râ♠❡tr♦s✱ ❞❡✈❡✲ s❡ ✈❡r✐✜❝❛r s❡ ♦ ♠♦❞❡❧♦ ❡s❝♦❧❤✐❞♦ s❡ ❛❥✉st❛✱ ❞❡ ❢❛t♦✱ ❛♦s ❞❛❞♦s ❞❡ ♠❛♥❡✐r❛ ❡❢❡t✐✈❛✱ ♣♦✐s ❡①✐st❡ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ q✉❡ ♦✉tr♦ ♠♦❞❡❧♦ ❆❘■▼❆ ❞❡s❡♠♣❡♥❤❡ ♦ ♠❡s♠♦ ♣❛♣❡❧✳ P❛r❛ ✐st♦✱ ♣♦❞❡✲s❡ r❡❛❧✐③❛r ✉♠ t❡st❡ s♦❜r❡ ♠♦❞❡❧♦ ❡s❝♦❧❤✐❞♦✱ ❛♥❛❧✐s❛♥❞♦ s❡ ♦s r❡sí❞✉♦s ❡st✐♠❛❞♦s ❞♦ ♠♦❞❡❧♦ sã♦ r✉í❞♦s ❜r❛♥❝♦s✳ ❙❡ s✐♠✱ ♣♦❞❡✲s❡ ❛❝❡✐t❛r ♦ ❛❥✉st❡ ❡s♣❡❝í✜❝♦❀ ❝❛s♦ ❝♦♥trár✐♦ ❞❡✈❡✲s❡ r❡♣❡t✐r ♦ ♣r♦❝❡ss♦❀
✹✳ Pr❡✈✐sã♦✿ ◆❛ ♠❛✐♦r✐❛ ❞❛s ✈❡③❡s✱ ❛s ♣r❡✈✐sõ❡s ♦❜t✐❞❛s ❝♦♠ ❡st❡ ♠ét♦❞♦s sã♦ ❞❡ ♠❛✐♦r ❝♦♥✜❛♥ç❛ ❞♦ q✉❡ ❛s ♦❜t✐❞❛s ♣♦r ♠❡✐♦ ❞❡ ♠♦❞❡❧❛❣❡♠ ❡❝♦♥♦♠étr✐❝❛ tr❛❞✐❝✐♦♥❛❧✳ ❉❡ q✉❛❧q✉❡r ♠♦❞♦✱ ❞❡✈❡✲s❡ ❝❤❡❝❛r ❝❛❞❛ ✉♠ ❞♦s ❝❛s♦s✳
✷✳✼ Pr♦❝❡ss♦s ❞❡ ♠❡♠ór✐❛ ❧♦♥❣❛
❍✉rst ✭✶✾✺✶✮✱ ✐❞❡♥t✐✜❝♦✉ ❡♠ s❡✉s ❡st✉❞♦s s♦❜r❡ ❤✐❞r♦❧♦❣✐❛✱ sér✐❡s ❝♦♠ ❝❛✲ r❛❝t❡ríst✐❝❛s ❞❡ ❧♦♥❣❛ ❞❡♣❡♥❞ê♥❝✐❛ ✭✐st♦ ❛❝♦♥t❡❝❡ q✉❛♥❞♦ ❤á ❝♦rr❡❧❛çã♦ ❡♥tr❡ ♦❜s❡r✈❛çõ❡s ✐♥t❡r❝❛❧❛❞❛s ♣♦r ✉♠ ❧♦♥❣♦ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦✮ ✭❈❍■❊PP❊✱ ✷✵✵✸✮✳ P❛r❛ ✐❞❡♥t✐✜❝❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ♠❡♠ór✐❛ ❧♦♥❣❛ ❡♠ sér✐❡s t❡♠♣♦r❛✐s✱ ❡❧❡ ✉t✐❧✐③♦✉✲s❡ ❞❡ ✉♠ ❝♦❡✜❝✐❡♥t❡ q✉❡ ❢♦✐ ❞❡♥♦♠✐♥❛❞♦ ✏❝♦❡✜❝✐❡♥t❡ ❞❡ ❍✉rst✑✳
▼♦t✐✈❛❞♦s ♣❡❧♦s tr❛❜❛❧❤♦s r❡❛❧✐③❛❞♦s ♣♦r ❍✉rst ✭✶✾✺✶✮✱ ▼❛♥❞❡❧❜r♦t ✫ ❚❛qq✉ ✭✶✾✼✾✮ ♣❛ss❛r❛♠ ❛ ❢❛③❡r ♦ ❡st✉❞♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ♣r♦❝❡ss♦s ❞❡ ♠❡♠ór✐❛ ❧♦♥❣❛ ❡♠ sér✐❡s ✜♥❛♥❝❡✐r❛s ✭❋❊❘❘❆❩✱ ✷✵✵✸✮✳
✷✾
♣❡rs✐stê♥❝✐❛ ♥❛s ❛✉t♦❝♦rr❡❧❛çõ❡s ♦❜s❡r✈❛❞❛s q✉❡✱ ❞❡❝❛❡♠ ❧❡♥t❛♠❡♥t❡ ♣❛r❛ ③❡r♦ ✭❙❖▲❉➪✱ ✷✵✵✽✮✳
❊st❡ ❢❡♥ô♠❡♥♦ ♥ã♦ ♣♦❞❡ s❡r ❞❡t❡❝t❛❞♦ ♣❡❧♦s ♠♦❞❡❧♦s ❞❛ ❝❧❛ss❡ ❆❘■▼❆ ✭♦ ♣❛râ♠❡tr♦ ❞❡ ❞✐❢❡r❡♥ç❛ ❛ss✉♠❡ ✈❛❧♦r❡s ✐♥t❡✐r♦s✮✱ ❞❡st❡ ♠♦❞♦✱ ●r❛♥❣❡r ✫ ❏♦②❡✉① ✭✶✾✽✵✮ ❡ ❍♦s❦✐♥❣ ✭✶✾✽✶✮ ♣r♦♣✉s❡r❛♠ ♦ ♠♦❞❡❧♦ ❆❘❋■▼❆ ✭❆✉t♦rr❡❣r❡ss✐✈♦ ❋r❛❝✐♦♥ár✐♦ ■♥t❡❣r❛❞♦ ❞❡ ▼é❞✐❛s ▼ó✈❡✐s✮✱ q✉❡ é ✉♠❛ ❣❡♥❡r❛❧✐③❛çã♦ ❞♦s ♠♦❞❡❧♦s ❆❘■▼❆✱ ✐st♦ é✱ q✉❡ ❞á ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞♦ ♣❛râ♠❡tr♦ ❞❡ ❞✐❢❡r❡♥ç❛ s❡r ❢r❛❝✐♦♥ár✐♦ ✭❋❊❘❘❆❩✱ ✷✵✵✸✮✳
✷✳✼✳✶ ▼♦❞❡❧♦ ❛✉t♦rr❡❣r❡ss✐✈♦ ❢r❛❝✐♦♥ár✐♦ ✐♥t❡❣r❛❞♦ ❞❡ ♠é❞✐❛s ♠ó✈❡✐s ✲ ❆❘✲ ❋■▼❆
❈♦♠♦ ❢♦✐ ❞✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ♦ ♠♦❞❡❧♦ ❆❘❋■▼❆ ❝♦♥s✐st❡ ❡♠ ✉♠ ♠♦❞❡❧♦ ❆❘■▼❆ ❝♦♠ ♦ ♣❛râ♠❡tr♦ d ❛❞❛♣t❛❞♦ ❞❡ ♠♦❞♦ q✉❡ ❛❝❡✐t❡ ♥ú♠❡r♦s ❢r❛❝✐♦♥ár✐♦s✳ ❆ ❞✐✲
❢❡r❡♥ç❛ ❝❛✉s❛❞❛ ❝♦♠ t❛❧ ❛❞❛♣t❛çã♦✱ é q✉❡ ❡st❡ ♥♦✈♦ ♠♦❞❡❧♦ ♣♦❞❡ ❝❛♣t❛r ♣r♦❝❡ss♦s ❝♦♠ ♠❡♠ór✐❛s ♠❛✐s ❧♦♥❣❛s q✉❡✱ ❡♠ ♦✉tr♦ ❝❛s♦✱ ♣r❡❝✐s❛r✐❛♠ s❡r ❡st✐♠❛❞♦s ✉t✐❧✐③❛♥❞♦ ♠✉✐t♦s ♣❛râ♠❡tr♦s ♥♦ ♠♦❞❡❧♦ ❆❘■▼❆ tr❛❞✐❝✐♦♥❛❧ ✭▲❊▼❖❙✱ ✷✵✶✹✮✳
◆♦ ♣r♦❝❡ss♦ ❆❘❋■▼❆✱ ❛s ❛✉t♦❝♦rr❡❧❛çõ❡s ♥ã♦ ❞❡❝❛❡♠ ❡①♣♦♥❡♥❝✐❛❧♠❡♥t❡ ❝♦♠♦ ♥♦ ♣r♦❝❡ss♦ ❆❘▼❆✱ ♠❛s ❤✐♣❡r❜♦❧✐❝❛♠❡♥t❡ ✭❍❖❙❑■◆●✱ ✶✾✽✶✮✳ ❆s ❛✉t♦❝♦rr❡❧❛çõ❡s ♣♦❞❡♠ s❡r s✐❣♥✐✜❝❛t✐✈❛s ♣♦r ❛té ❝❡♥t❡♥❛s ❞❡ ❧❛❣s❀ ❡st❛ ❝❛r❛❝t❡ríst✐❝❛ é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ♠❡♠ór✐❛ ❧♦♥❣❛ ❡ ♠♦❞❡❧♦s ❆❘❋■▼❆ sã♦ ♦s ♠❛✐s ✐♥❞✐❝❛❞♦s ♣❛r❛ ♠♦❞❡❧❛r sér✐❡s ❝♦♠ ❡st❡ ❝♦♠♣♦rt❛♠❡♥t♦ ✭●❖▼❊❙✱ ✷✵✵✺✮✳
❆♥❛❧✐s❛♥❞♦✲s❡ ❣r❛✜❝❛♠❡♥t❡ ❛ ❢✉♥çã♦ ❞❡ ❛✉t♦❝♦rr❡❧❛çã♦✱ ♣♦❞❡✲s❡ ♦❜s❡r✈❛r q✉❡ ❡①✐st❡ ♠❡♠ór✐❛ ❧♦♥❣❛ q✉❛♥❞♦ ❛s ❢✉♥çõ❡s ❞❡ ❛✉t♦❝♦rr❡❧❛çã♦ ❛♠♦str❛✐s ♣♦ss✉❡♠ ❞❡❝❛✐♠❡♥t♦ ❧❡♥t♦✱ ♦ q✉❡ ♠♦str❛ ❛ ♣❡rs✐stê♥❝✐❛ ❞❛ sér✐❡✳
◆♦ ❞❡❝♦rr❡r ❞♦s ❛♥♦s ❢♦r❛♠ ❛♣r❡s❡♥t❛❞♦s ♠✉✐t♦s ❡st✐♠❛❞♦r❡s ❞♦ ♣❛râ♠❡tr♦ ❞❡ ❧♦♥❣❛ ❞❡♣❡♥❞ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❢♦r❛♠ ❞✐✈✐❞✐❞❛s ❞✉❛s ❛❜♦r❞❛❣❡♥s ❞✐st✐♥t❛s✿ ❛ ♣❛r❛♠étr✐❝❛ ❡ ❛ s❡♠✐✲♣❛r❛♠étr✐❝❛✳
◆❛ ❛❜♦r❞❛❣❡♠ ♣❛r❛♠étr✐❝❛✱ t♦❞♦s ♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ sã♦ ❡st✐♠❛❞♦s s✐♠✉❧t❛♥❡❛♠❡♥t❡❀ ♦s ❡st✐♠❛❞♦r❡s q✉❡ s❡❣✉❡♠ ✉t✐❧✐③❛♥❞♦ ❡st❡ ♠ét♦❞♦ ♠♦str❛♠ r❡s✉❧t❛❞♦s ❡✜❝❛③❡s ❛té ❤♦❥❡✱ ❡♠❜♦r❛ ❡①✐❥❛♠ ❛❧t♦ ❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧✳
