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On L2 modulus of continuity of Brownian local times and Riesz potentials
Deya, Aurelien Nualart, David Tindel, Samy
Deya, Aurelien
Nualart, David
Tindel, Samy
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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 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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2015-05-05
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Institute of Mathematical Statistics
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nualart_modulus.pdf
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Keywords
Brownian motion, Local time, Malliavin calculus
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.