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## Donsker Theorem and its application

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**DonskerTheorem and its application**VadymOmelchenko**Proof (Proof of the Lemma)**• Hence both (A) and (B) imply (3) which is the affirmation of the theorem. QED**Proof**• Having proved the assertion of this theorem for finite-dimensional distributions and having proved the tightness we have proved the theorem. QED**Unit Dimension {-1,+1}**• N=20 N=60 • N=1000**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