The heat equation and reflected Brownian motion in time-dependent domains

• Krzysztof Burdzy ^[1] ; Zhen-Qing Che ^[1] ; John Sylvester ^[1]
  1. [1] University of Washington

     University of Washington

     Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 32, Nº. 1, 2, 2004, págs. 775-804
• Idioma: inglés
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• Resumen

  • The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as "noncylindrical domains,'' and its connections with partial differential equations. Construction is given for RBM in C3-smooth time-dependent domains in the n-dimensional Euclidean space \Rn. We present various sample path properties of the process, two-sided estimates for its transition density function, and a probabilistic representation of solutions to some partial differential equations. Furthermore, the one-dimensional case is thoroughly studied, with the assumptions on the smoothness of the boundary drastically relaxed.