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Donsker Theorem and its application. Vadym Omelchenko. Definition. Donsker Theorem. Proof. Proof. Proof. Proof. Proof. Proof of the tightness. Proof (Proof of the Lemma). Proof (Proof of the Lemma). Proof (Proof of the Lemma).

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Donsker theorem and its application l.jpg

DonskerTheorem and its application

VadymOmelchenko



Donsker theorem l.jpg
Donsker Theorem










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Proof (Proof of the Lemma)

  • Hence both (A) and (B) imply (3) which is the affirmation of the theorem. QED




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Proof

  • Having proved the assertion of this theorem for finite-dimensional distributions and having proved the tightness we have proved the theorem. QED


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Application of Donsker Theorem


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Unit Dimension {-1,+1}

  • N=20 N=60

  • N=1000


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Application of Donsker’s Theorem

  • More important than this qualitative interpretation is the use of Donsker's theorem to prove limit theorems for various functions of the partial sums


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Application of Donsker’s Theorem
















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