Reflecting Brownian snake and a Neumann-Dirichlet problem

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:89

Article

Abraham, R

关键词: Brownian snake;    reflecting Brownian motion;    semi-linear partial differential equations;    Neumann problem;   

DOI  :  10.1016/S0304-4149(00)00027-2

来源: Elsevier

【 摘 要 】

The paper deals with a path-valued Markov process: the reflecting Brownian snake. It is a particular case of the path-valued process previously introduced by Le Gall. Here the spatial motion is a reflecting Brownian motion in a domain D of R-d. Using this probabilistic tool, we construct an explicit function upsilon solution of an integral equation which is, under some hypotheses on the regularity of upsilon, equivalent to a semi-linear partial differential equation in D with some mixed Neumann-Dirichlet conditions on the boundary. When the hypotheses on upsilon are not satisfied, we prove that upsilon is still solution of a weak formulation of the Neumann-Dirichlet problem. (C) 2000 Elsevier Science B.V. All rights reserved.

【 授权许可】

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