A CLT for the L modulus of continuity of Brownian local time
نویسندگان
چکیده
Let {Lt ; (x, t) ∈ R1 ×R1 +} denote the local time of Brownian motion and αt := ∫ ∞ −∞ (Lt ) 2 dx. Let η = N(0, 1) be independent of αt. For each fixed t ∫∞ −∞(L x+h t − Lt )2 dx− 4ht h3/2 L → ( 64 3 )1/2 √ αt η, as h → 0. Equivalently ∫∞ −∞(L x+1 t − Lt )2 dx− 4t t3/4 L → ( 64 3 )1/2 √ α1 η, as t → ∞.
منابع مشابه
A Clt for the L2 Modulus of Continuity of Brownian Local Time1 By
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 o...
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