360 likes | 861 Views
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).
E N D
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