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

Aurélien Deya; David Nualart; Samy Tindel

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arXiv · 1304.4558

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

Aurélien Deya·David Nualart·Samy Tindel

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Abstract

This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on 3 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 L2 modulus of continuity for a 1-dimensional Brownian motion. (c) Extension of the second result to a 2-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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Aurélien Deya, David Nualart, Samy Tindel. 2013-04-16. On L2 modulus of continuity of Brownian local times and Riesz potentials. https://arxiv.org/abs/1304.4558

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