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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
- Page 1 and 2: The Contra
- Page 3 and 4: Quickselect / Find Task: Given a li
- Page 5 and 6: Quickselect / Find Task: Given a li
- Page 7 and 8: For simplicity k = 1. Quickselect /
- Page 9 and 10: For simplicity k = 1. Quickselect /
- Page 11 and 12: Recursive equation Yn := Xn n A pos
- Page 13 and 14: Contraction Hennin
- Page 15 and 16: For µ, ν ∈ M1(R) let Co
- Page 17: Contraction Proof:
- Page 21 and 22: The stochastic fix
- Page 23 and 24: Donsker’s Theore
- Page 25 and 26: Donsker’s Theore
- Page 27 and 28: S n t = 1 √ n ⎛ ⌊nt⌋ ⎝ D
- Page 29 and 30: In space: Decomposition of Brownian
- Page 31 and 32: In space: B −1.5 −0.5 0.5 1.0 1
- Page 33 and 34: It holds Decomposition of Brownian
- Page 35 and 36: In time: B −1.5 −0.5 0.5 1.0 1.
- Page 37 and 38: (Bt) t Decomposition of Brownian Mo
- Page 39 and 40: Theorem (Uniquenes
- Page 41 and 42: S_1 Time-decomposition of the rando
- Page 43 and 44: Time-decomposition of the random wa
- Page 45 and 46: The Zolotarev metr
- Page 47 and 48: The Zolotarev metr
- Page 49 and 50: Properties of the Zolotarev distanc
- Page 51 and 52: Lemma Properties of the Zolotarev d
- Page 53 and 54: Proof of Donsker’s The</s
- Page 55 and 56: Proof of Donsker’s The</s
- Page 57 and 58: Properties of ζs in C([0, 1]) Henn
- Page 59 and 60: Theorem Properties
<str<strong>on</strong>g>C<strong>on</strong>tracti<strong>on</strong></str<strong>on</strong>g><br />
Proof: Let X , Y s.t. L(X ) = µ, L(Y ) = ν <strong>and</strong><br />
<str<strong>on</strong>g>The</str<strong>on</strong>g>n<br />
E[|X − Y |] ≤ d(µ, ν) + ε.<br />
ℓ1(F (µ), F (ν)) ≤ E[|UX + 1 − (UY + 1)|] = EUE[|X − Y |]<br />
≤ EU(ℓ1(µ, ν) + ε).<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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