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

• Deya, Aurélien ^[1] ; Nualart, David ^[2] ; Tindel, Samy ^[1]
  1. [1] University of Lorraine

     University of Lorraine

     Arrondissement de Nancy, Francia

     
  2. [2] University of Kansas

     University of Kansas

     City of Lawrence, Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 3, 2015, págs. 1493-1534
• Idioma: inglés
• DOI: 10.1214/13-AOP904
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• Resumen

  • 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 L2 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.