The Annals of Probability

On L2 modulus of continuity of Brownian local times and Riesz potentials

Aurélien Deya, David Nualart, and Samy Tindel

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This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on three closely related problems: (a) Limit theorem for a Brownian modulus of continuity involving Riesz potentials, where the limit law is an intricate Gaussian mixture. (b) Central limit theorems for the projections of $L^{2}$ modulus of continuity for a one-dimensional Brownian motion. (c) Extension of the second result to a two-dimensional Brownian motion. Our proofs rely on a combination of stochastic calculus and Malliavin calculus tools, plus a thorough analysis of singular integrals.

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Ann. Probab., Volume 43, Number 3 (2015), 1493-1534.

First available in Project Euclid: 5 May 2015

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Zentralblatt MATH identifier

Primary: 60G15: Gaussian processes 60H07: Stochastic calculus of variations and the Malliavin calculus 60H10: Stochastic ordinary differential equations [See also 34F05] 65C30: Stochastic differential and integral equations

Brownian motion local time Malliavin calculus


Deya, Aurélien; Nualart, David; Tindel, Samy. On L 2 modulus of continuity of Brownian local times and Riesz potentials. Ann. Probab. 43 (2015), no. 3, 1493--1534. doi:10.1214/13-AOP904.

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