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 R d . 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.
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