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Reflecting Brownian snake and a Neumann-Dirichlet problem

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  • Abraham, Romain

Abstract

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 . 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, equivalent to a semi-linear partial differential equation in D with some mixed Neumann-Dirichlet conditions on the boundary. When the hypotheses on v are not satisfied, we prove that v is still solution of a weak formulation of the Neumann-Dirichlet problem.

Suggested Citation

  • Abraham, Romain, 2000. "Reflecting Brownian snake and a Neumann-Dirichlet problem," Stochastic Processes and their Applications, Elsevier, vol. 89(2), pages 239-260, October.
    • Handle: RePEc:eee:spapps:v:89:y:2000:i:2:p:239-260
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