The Heat Equation and Reflected Brownian Motion in Time-dependent Domains
نویسندگان
چکیده
The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as “non-cylindrical domains,” and its connections with partial differential equations. Construction is given for reflecting Brownian motion in C-smooth time-dependent domains in the n-dimensional Euclidean space R. Various sample path properties of RBM, its two-sided transition density functions estimate and the probabilistic representation of solutions for the corresponding partial differential equations are obtained. Furthermore, the onedimensional case is throughly studied, with the assumptions on the smoothness of the boundary drastically relaxed. Short Title: Reflecting Brownian Motion in Time-dependent Domains
منابع مشابه
The Heat Equation and Reflected Brownian Motion in Time-dependent Domains by Krzysztof Burdzy,1
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 i...
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