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May 2015 On L2 modulus of continuity of Brownian local times and Riesz potentials
Aurélien Deya, David Nualart, Samy Tindel
Ann. Probab. 43(3): 1493-1534 (May 2015). DOI: 10.1214/13-AOP904


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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Aurélien Deya. David Nualart. Samy Tindel. "On L2 modulus of continuity of Brownian local times and Riesz potentials." Ann. Probab. 43 (3) 1493 - 1534, May 2015.


Published: May 2015
First available in Project Euclid: 5 May 2015

zbMATH: 1326.60112
MathSciNet: MR3342669
Digital Object Identifier: 10.1214/13-AOP904

Primary: 60G15 , 60H07 , 60H10 , 65C30

Keywords: Brownian motion , Local time , Malliavin calculus

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 3 • May 2015
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