ON L2 MODULUS OF CONTINUITY OF BROWNIAN LOCAL TIMES AND RIESZ POTENTIALS

• 成果类型: Article
• 署名作者: Deya, Aurelien; Nualart, David; Tindel, Samy
• 署名单位: Universite de Lorraine; University of Kansas
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP904
• 发表日期: 2015
• 页码: 1493-1534
• 关键词: CENTRAL-LIMIT-THEOREM; multiple stochastic integrals; REPRESENTATION; motion

摘要

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.