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Stochastic differential equations for multi-dimensional domain with reflecting boundary. (English) Zbl 0591.60049

We prove that there exists a unique solution of the Skorohod equation for a domain in \(R^ d\) with reflecting boundary condition. We remove the admissibility condition of the domain which is assumed in the work of P. L. Lions and A. S. Sznitman, Stochastic differential equations with reflecting boundary conditions. Commun. Pure Appl. Math. 37, 511-537 (1984). We first consider a deterministic case and then discuss a stochastic case.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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