On L2 modulus of continuity of Brownian local times and Riesz potentials
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Issue Date
2015-05-05Author
Deya, Aurelien
Nualart, David
Tindel, Samy
Publisher
Institute of Mathematical Statistics
Type
Article
Article Version
Scholarly/refereed, publisher version
Metadata
Show full item recordAbstract
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 L2L2 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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Citation
Deya, Aurélien, David Nualart, and Samy Tindel. "On L2 Modulus of Continuity of Brownian Local times and Riesz Potentials." The Annals of Probability 43.3 (2015): 1493-534.
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