A Clt for the L2 Modulus of Continuity of Brownian Local Time1 By
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چکیده
Let {L x t ; (x, t) ∈ R 1 × R 1 + } denote the local time of Brownian motion, and α t := ∞ −∞ (L x t) 2 dx. Let η = N(0, 1) be independent of α t. For each fixed t, ∞ −∞ (L x+h t − L x t) 2 dx − 4ht h 3/2 L → 64 3 1/2 √ α t η as h → 0. Equivalently, ∞ −∞ (L x+1 t − L x t) 2 dx − 4t t 3/4 L → 64 3 1/2 √ α 1 η as t → ∞. 1. Introduction. In [10] almost sure limits are obtained for the L p moduli of continuity of local times of a very wide class of symmetric Lévy processes. For Brownian motion the result is as follows: Let {L x t ; (x, t) ∈ R 1 × R 1 + } denote the local time of Brownian motion. Then for all p ≥ 1, and all t ∈ R + ,
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On L2 Modulus of Continuity of Brownian Local times and Riesz Potentials by Aurélien Deya,
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