Boundary behavior of a constrained Brownian motion between reflecting-repellent walls
Stochastic variational inequalities provide a unified treatment for stochastic differential equations living in a closed domain with normal reflection and/or singular repellent drift. When the domain is a convex polyhedron, we prove that the reflected-repelled Brownian motion does not hit the non-smooth part of the boundary. A sufficient condition for nonhitting a face of the polyhedron is derived from the one-dimensional situation. A full answer to the question of attainability of the walls of the Weyl chamber may be given for a radial Dunkl process.
2000 AMS Mathematics Subject Classification: Primary: 60G17; Secondary: 60H10.