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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
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S n t = 1<br />
√ n<br />
⎛<br />
⌊nt⌋ <br />
⎝<br />
D<strong>on</strong>sker’s <str<strong>on</strong>g>The</str<strong>on</strong>g>orem<br />
k=1<br />
<str<strong>on</strong>g>The</str<strong>on</strong>g>orem (D<strong>on</strong>sker, 1951)<br />
Xk + (nt − ⌊nt⌋)X ⌊nt⌋+1<br />
⎞<br />
⎠ , t ∈ [0, 1]<br />
S n d → B in (C([0, 1]), || · ||sup), where B is a st<strong>and</strong>ard Brownian<br />
Moti<strong>on</strong>.<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
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