The Contraction Method on C([0,1]) and Donsker's ... - Eurandom
The Contraction Method on C([0,1]) and Donsker's ... - Eurandom
The Contraction Method on C([0,1]) and Donsker's ... - Eurandom
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Proof of D<strong>on</strong>sker’s <str<strong>on</strong>g>The</str<strong>on</strong>g>orem (Sketch)<br />
An c<strong>on</strong>tracti<strong>on</strong> argument shows<br />
for δ < ε/2. Together with<br />
ζ2+ε(S n , B n ) = O(n −δ )<br />
||B n − B|| → 0 a.s.<br />
D<strong>on</strong>sker’s <str<strong>on</strong>g>The</str<strong>on</strong>g>orem follows with the following properties of<br />
Zolotarev’s distance.<br />
Henning Sulzbach J. W. Goethe-Universität Frankfurt a. M. <str<strong>on</strong>g>The</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>tracti<strong>on</strong></str<strong>on</strong>g> <str<strong>on</strong>g>Method</str<strong>on</strong>g> <strong>on</strong> C([0, 1]) <strong>and</strong> D<strong>on</strong>sker’s <str<strong>on</strong>g>The</str<strong>on</strong>g>orem