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

• 成果类型: Article
• 署名作者: Burdzy, K; Chen, ZQ; Sylvester, J
• 署名单位: University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2004
• 页码: 775-804
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; boundary-conditions; diffusion-processes; oblique reflection; lipschitz-domains; DECOMPOSITION; THEOREM; holder

摘要

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 C-3-smooth time-dependent domains in the n-dimensional Euclidean space R-n. 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.