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On stochastic differential equations with reflecting boundary condition in convex domains

Łaukajtys W.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 4

445-455

Let D be an open convex set in R^d and let F be a Lipschitz operator defined on the space of adapted cadlag processes. We show that for any adapted process H and any semimartingale Z there exists a unique strong solution of the following stochastic differential equation (SDE) with reflection on the boundary of D: Xt=Ht + integral of (F(X)s-, dZs] on the interval [0, t]+Kt, t belongs to R+. Our proofs are based on new a priori estimates for solutions of the deterministic Skorokhod problem.