## The Annals of Probability

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

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 5 May 2015

https://projecteuclid.org/euclid.aop/1430830288

Digital Object Identifier
doi:10.1214/13-AOP904

Mathematical Reviews number (MathSciNet)
MR3342669

Zentralblatt MATH identifier
1326.60112

#### Citation

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. https://projecteuclid.org/euclid.aop/1430830288

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