Reeecting Brownian Snake and a Neumann-dirichlet Problem
نویسنده
چکیده
The paper deals with a Markov path-valued process : the reeecting Brownian snake. It is a particular case of the path-valued process former introduced by Le Gall. Here the spatial motion (which is for Le Gall any Markov process) is a reeecting Brownian motion in a domain D of R d. Using this probabilistic tool, we construct an explicit function v solution of an integral equation which is, under some hypothesis on the regularity of v, equivalent to a semi-linear partial diierential equation in D with some mixed Neumann-Dirichlet conditions on the boundary. As the hypothesis on v are not always veriied, we also prove that v is solution of a weak formulation of the Neumann-Dirichlet problem.
منابع مشابه
Re ecting Brownian snake and a Neumann–Dirichlet problem
The paper deals with a path-valued Markov process: the re ecting Brownian snake. It is a particular case of the path-valued process previously introduced by Le Gall. Here the spatial motion is a re ecting Brownian motion in a domain D of R. Using this probabilistic tool, we construct an explicit function v solution of an integral equation which is, under some hypotheses on the regularity of v, ...
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