The skorokhod oblique reflection problem in a convex polyhedron

Abstract

The Skorokhod oblique resection problem is studied in the case of n-dimensional convex polyhedral domains. The natu- ral sucient condition on the resection directions is found, which together with the Lipschitz condition on the coecients gives the existence and uniqueness of the solution. The continuity of the cor- responding solution mapping is established. This property enables one to construct in a direct way the resected (in a convex polyhedral domain) diusion processes possessing the nice properties.