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  1. ❋♦r♠❛❧✐③❛t✐♦♥ ♦❢ r❡❧❛t✐♦♥s ❜❡t✇❡❡♥ ❝✉♠✉❧❛t✐✈❡ ❝✉r✈❡s ❛♥❞ ❡✈❡♥t str❡❛♠s✿ ❢r♦♠ ♥❡t✇♦r❦ ❝❛❧❝✉❧✉s t♦ ❈P❆✱ ❛♥❞ ❜❛❝❦ ▼❛r❝ ❇♦②❡r ✶✱✯ ✱ P✐❡rr❡ ❘♦✉① ✶ ✱ ▲❡♦♥✐❡ ❑ö❤❧❡r ✷ ✱ ❇♦r✐s❧❛✈ ◆✐❦♦❧✐❝ ✷ ✱ ❘♦❧❢ ❊r♥st ✷ ✺t❤ ❲♦r❦s❤♦♣ ♦♥ ◆❡t✇♦r❦ ❈❛❧❝✉❧✉s ✭❲♦◆❡❈❛✲✺✮ ❖❝t♦❜❡r ✾t❤ ✷✵✷✵ 1 ❖◆❊❘❆✱ 2 ❚❯ ❇r❛✉♥s❝❤✇❡✐❣

  2. ◆❈✴❈P❆ ❖✉t❧✐♥❡ ✶ ❈✉r✈❡ ❜❛s❡❞ ♠♦❞❡❧s ✷ ❆ ❣❡♥❡r❛❧ ♠♦❞❡❧✱ ❛♥❞ ✐ts t♦♦❧s ❚❤❡ ♠♦❞❡❧ ❚❤❡ t♦♦❧s ✸ ❘❡s✉❧ts ❋r♦♠ ◆❈ t♦ ❈P❆✱ ❛♥❞ ❜❛❝❦ P❛❝❦❡t✐③❡r✿ ❣❡♥❡r❛❧✐s✐♥❣ ♣r❡✈✐♦✉s r❡s✉❧ts ❈P❆ ✐♥t❡❣r❛t✐♦♥ ❆❣❣r❡❣❛t✐♦♥ ✹ ❈♦♥❝❧✉s✐♦♥ ✺ ❇✐❜❧✐♦❣r❛♣❤② ❇♦②❡r✱ ❘♦✉①✱ ✶✴✶✽ ◆❈✴❈P❆ ❖❝t✳ ✾t❤ ✷✵✷✵

  3. ❖✉t❧✐♥❡ ✶ ❈✉r✈❡ ❜❛s❡❞ ♠♦❞❡❧s ✷ ❆ ❣❡♥❡r❛❧ ♠♦❞❡❧✱ ❛♥❞ ✐ts t♦♦❧s ✸ ❘❡s✉❧ts ✹ ❈♦♥❝❧✉s✐♦♥ ✺ ❇✐❜❧✐♦❣r❛♣❤②

  4. ◆❈✴❈P❆ ❈✉r✈❡ ❜❛s❡❞ ♠♦❞❡❧s ❈✉r✈❡ ❜❛s❡❞ ♠♦❞❡❧s ◆❈ ◆❡t✇♦r❦ ❝❛❧❝✉❧✉s ✉♣♣❡r✴❧♦✇❡r ❛rr✐✈❛❧ ❝✉r✈❡s ✭str✐❝t✮ ♠✐♥✐♠❛❧ ✭♠❛①✐♠❛❧✮ ❚❤r❡❡ ♠♦❞❡❧s s❡r✈✐❝❡ ❝✉r✈❡ s❤❛♣✐♥❣ ❝✉r✈❡s ❘❡❧❛t✐♦♥ ❘❚❈ ↔ ◆❈ ❘❚❈ ❘❡❛❧✲❚✐♠❡ ❝❛❧❝✉❧✉s ❡q✉✐✈❛❧❡♥❝❡ ❬✶✱ ✷❪ ✉♣ t♦ t❡❝❤♥✐❝❛❧ ❞❡t❛✐❧s ✉♣♣❡r✴❧♦✇❡r ❛rr✐✈❛❧ ❝✉r✈❡s ✉♣♣❡r✴❧♦✇❡r s❡r✈✐❝❡ ❝✉r✈❡s ❘❡❧❛t✐♦♥s ❈P❆ ↔ ◆❈ ❣r❡❡❞② s❤❛♣❡rs q✉✐t❡ t❤❡ s❛♠❡ ♠♦❞❡❧s ♦❢ ❈P❆ ❈♦♠♣♦s✐t✐♦♥❛❧ P❡r❢♦r♠❛♥❝❡ ✇♦r❦❧♦❛❞ ❬✸✱ ✹❪ ❆♥❛❧②s✐s ❞✐✛❡r❡♥t ❛♥❛❧②s✐s ♠❡t❤♦❞s ❡✈❡♥t str❡❛♠ ❡✈❡♥t ❞✐st❛♥❝❡ ❜✉s② ✇✐♥❞♦✇ ❇♦②❡r✱ ❘♦✉①✱ ✷✴✶✽ ◆❈✴❈P❆ ❖❝t✳ ✾t❤ ✷✵✷✵

  5. ❖✉t❧✐♥❡ ✶ ❈✉r✈❡ ❜❛s❡❞ ♠♦❞❡❧s ✷ ❆ ❣❡♥❡r❛❧ ♠♦❞❡❧✱ ❛♥❞ ✐ts t♦♦❧s ❚❤❡ ♠♦❞❡❧ ❚❤❡ t♦♦❧s ✸ ❘❡s✉❧ts ✹ ❈♦♥❝❧✉s✐♦♥ ✺ ❇✐❜❧✐♦❣r❛♣❤②

  6. ❖✉t❧✐♥❡ ✶ ❈✉r✈❡ ❜❛s❡❞ ♠♦❞❡❧s ✷ ❆ ❣❡♥❡r❛❧ ♠♦❞❡❧✱ ❛♥❞ ✐ts t♦♦❧s ❚❤❡ ♠♦❞❡❧ ❚❤❡ t♦♦❧s ✸ ❘❡s✉❧ts ✹ ❈♦♥❝❧✉s✐♦♥ ✺ ❇✐❜❧✐♦❣r❛♣❤②

  7. ◆❈✴❈P❆ ❆ ❣❡♥❡r❛❧ ♠♦❞❡❧✱ ❛♥❞ ✐ts t♦♦❧s ❚❤❡ ♠♦❞❡❧ ❚✇♦ ✢♦✇✴❝♦♠♣♦♥❡♥t ♠♦❞❡❧s ❊✈❡♥t ❙tr❡❛♠✴❈P❆ ◆❡t✇♦r❦ ❈❛❧❝✉❧✉s E ′ A ′ E A C C ❋❧♦✇ ♠♦❞❡❧ E ( t ) ✿ ♥✉♠❜❡r ♦❢ ❡✈❡♥ts ✉♣ t♦ A ( t ) ✿ ❛♠♦✉♥t ♦❢ ❞❛t❛ ✉♣ t♦ t✐♠❡ t t✐♠❡ t η + , η − ✿ α u , α l ✿ ❈♦♥tr❛❝t ❡✈❡♥t ❛rr✐✈❛❧ ❢✉♥❝✲ ✉♣♣❡r ❛♥❞ ❧♦✇❡r ❛r✲ t✐♦♥s r✐✈❛❧ ❝✉r✈❡s ∀ t, d ≥ 0 E ( t + d ) − E ( t ) ≤ η + ( d ) α l ( d ) ≤ A ( t + d ) − A ( t ) ≤ α u ( d ) E ( t + d ) − E ( t ) ≥ η − ( d ) ❋❧♦✇ tr❛♥s❢♦r✲ ❇✉s② ✇✐♥❞♦✇ ❘❡s✐❞✉❛❧ s❡r✈✐❝❡ ♠❛t✐♦♥ ❇♦②❡r✱ ❘♦✉①✱ ✸✴✶✽ ◆❈✴❈P❆ ❖❝t✳ ✾t❤ ✷✵✷✵

  8. ◆❈✴❈P❆ ❆ ❣❡♥❡r❛❧ ♠♦❞❡❧✱ ❛♥❞ ✐ts t♦♦❧s ❚❤❡ ♠♦❞❡❧ ❚❤❡ ❣❧♦❜❛❧ ♣✐❝t✉r❡ ❇♦②❡r✱ ❘♦✉①✱ ✹✴✶✽ ◆❈✴❈P❆ ❖❝t✳ ✾t❤ ✷✵✷✵

  9. ◆❈✴❈P❆ ❆ ❣❡♥❡r❛❧ ♠♦❞❡❧✱ ❛♥❞ ✐ts t♦♦❧s ❚❤❡ ♠♦❞❡❧ ❆ ♣❛❝❦❡t ❢✉♥❝t✐♦♥ ❛s ❣❛t❡✇❛② ❆rr✐✈❛❧ ❝✉r✈❡ P❛❝❦❡t ❝♦✉♥t ❊✈❡♥t ❝♦✉♥t A : R + → R + P : R + → N E : R + → N A ( t ) ✿ ❛♠♦✉♥t ♦❢ ❞❛t❛ ✉♣ P ( d ) ✿ ♥✉♠❜❡r ♦❢ ❢✉❧❧ E ( t ) ✿ ♥✉♠❜❡r ♦❢ ❢✉❧❧ t♦ t ♣❛❝❦❡ts ✐♥ t❤❡ d ✜rst ♣❛❝❦❡ts ✉♣ t♦ t ✏❜✐ts✑ NC CP A ���� ���� P ( A ) = E � �� � ❬✺❪ ❇♦②❡r✱ ❘♦✉①✱ ✺✴✶✽ ◆❈✴❈P❆ ❖❝t✳ ✾t❤ ✷✵✷✵

  10. ◆❈✴❈P❆ ❆ ❣❡♥❡r❛❧ ♠♦❞❡❧✱ ❛♥❞ ✐ts t♦♦❧s ❚❤❡ ♠♦❞❡❧ ■❧❧✉str❛t✐♦♥ A ( t ) E ( t ) P ( d ) ✹ ✹ ✹ ✸ ✸ ✸ ✷ ✷ ✷ ✶ ✶ ✶ t t ✶ ✷ ✸ ✹ ✶ ✷ ✸ ✹ ✶ ✷ ✸ ✹ ❞ ❙❝❡♥❛r✐♦✿ ❋✐rst ♣❛❝❦❡t✿ s✐③❡ ✶✱ t❤r♦✉❣❤♣✉t ✶ ❙❡❝♦♥❞ ♣❛❝❦❡t✿ s✐③❡ ✶✱ t❤r♦✉❣❤♣✉t ✶✴✷ ❚❤✐r❞ ♣❛❝❦❡t✿ s✐③❡ ✷✱ t❤r♦✉❣❤♣✉t ✷ ❋♦✉rt❤ ♣❛❝❦❡t✿ s✐③❡ ✶✱ t❤r♦✉❣❤♣✉t ✶ ❇♦②❡r✱ ❘♦✉①✱ ✻✴✶✽ ◆❈✴❈P❆ ❖❝t✳ ✾t❤ ✷✵✷✵

  11. ◆❈✴❈P❆ ❆ ❣❡♥❡r❛❧ ♠♦❞❡❧✱ ❛♥❞ ✐ts t♦♦❧s ❚❤❡ ♠♦❞❡❧ ■❧❧✉str❛t✐♦♥ A ( t ) E ( t ) P ( d ) ✹ ✹ ✹ ✸ ✸ ✸ ✷ ✷ ✷ ✶ ✶ ✶ t t ✶ ✷ ✸ ✹ ✶ ✷ ✸ ✹ ✶ ✷ ✸ ✹ ❞ ❙❝❡♥❛r✐♦✿ ❋✐rst ♣❛❝❦❡t✿ s✐③❡ ✶✱ t❤r♦✉❣❤♣✉t ✶ ❙❡❝♦♥❞ ♣❛❝❦❡t✿ s✐③❡ ✶✱ t❤r♦✉❣❤♣✉t ✶✴✷ ❚❤✐r❞ ♣❛❝❦❡t✿ s✐③❡ ✷✱ t❤r♦✉❣❤♣✉t ✷ ❋♦✉rt❤ ♣❛❝❦❡t✿ s✐③❡ ✶✱ t❤r♦✉❣❤♣✉t ✶ ❇♦②❡r✱ ❘♦✉①✱ ✻✴✶✽ ◆❈✴❈P❆ ❖❝t✳ ✾t❤ ✷✵✷✵

  12. ◆❈✴❈P❆ ❆ ❣❡♥❡r❛❧ ♠♦❞❡❧✱ ❛♥❞ ✐ts t♦♦❧s ❚❤❡ ♠♦❞❡❧ ■❧❧✉str❛t✐♦♥ A ( t ) E ( t ) P ( d ) ✹ ✹ ✹ ✸ ✸ ✸ ✷ ✷ ✷ ✶ ✶ ✶ t t ✶ ✷ ✸ ✹ ✶ ✷ ✸ ✹ ✶ ✷ ✸ ✹ ❞ ❙❝❡♥❛r✐♦✿ ❋✐rst ♣❛❝❦❡t✿ s✐③❡ ✶✱ t❤r♦✉❣❤♣✉t ✶ ❙❡❝♦♥❞ ♣❛❝❦❡t✿ s✐③❡ ✶✱ t❤r♦✉❣❤♣✉t ✶✴✷ ❚❤✐r❞ ♣❛❝❦❡t✿ s✐③❡ ✷✱ t❤r♦✉❣❤♣✉t ✷ ❋♦✉rt❤ ♣❛❝❦❡t✿ s✐③❡ ✶✱ t❤r♦✉❣❤♣✉t ✶ ❇♦②❡r✱ ❘♦✉①✱ ✻✴✶✽ ◆❈✴❈P❆ ❖❝t✳ ✾t❤ ✷✵✷✵

  13. ◆❈✴❈P❆ ❆ ❣❡♥❡r❛❧ ♠♦❞❡❧✱ ❛♥❞ ✐ts t♦♦❧s ❚❤❡ ♠♦❞❡❧ ■❧❧✉str❛t✐♦♥ A ( t ) E ( t ) P ( d ) ✹ ✹ ✹ ✸ ✸ ✸ ✷ ✷ ✷ ✶ ✶ ✶ t t ✶ ✷ ✸ ✹ ✶ ✷ ✸ ✹ ✶ ✷ ✸ ✹ ❞ ❙❝❡♥❛r✐♦✿ ❋✐rst ♣❛❝❦❡t✿ s✐③❡ ✶✱ t❤r♦✉❣❤♣✉t ✶ ❙❡❝♦♥❞ ♣❛❝❦❡t✿ s✐③❡ ✶✱ t❤r♦✉❣❤♣✉t ✶✴✷ ❚❤✐r❞ ♣❛❝❦❡t✿ s✐③❡ ✷✱ t❤r♦✉❣❤♣✉t ✷ ❋♦✉rt❤ ♣❛❝❦❡t✿ s✐③❡ ✶✱ t❤r♦✉❣❤♣✉t ✶ ❇♦②❡r✱ ❘♦✉①✱ ✻✴✶✽ ◆❈✴❈P❆ ❖❝t✳ ✾t❤ ✷✵✷✵

  14. ❖✉t❧✐♥❡ ✶ ❈✉r✈❡ ❜❛s❡❞ ♠♦❞❡❧s ✷ ❆ ❣❡♥❡r❛❧ ♠♦❞❡❧✱ ❛♥❞ ✐ts t♦♦❧s ❚❤❡ ♠♦❞❡❧ ❚❤❡ t♦♦❧s ✸ ❘❡s✉❧ts ✹ ❈♦♥❝❧✉s✐♦♥ ✺ ❇✐❜❧✐♦❣r❛♣❤②

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