BOUNDARY BEHAVIOR OF A CONSTRAINED BROWNIAN MOTION
BETWEEN REFLECTING-REPELLENT WALLS
Abstract: 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
non-hitting 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.
oundary behavior of a constrained Brownian motion between reflecting-repellent walls
ominique Lépingle
Keywords and phrases: Multivalued stochastic differential equation, reflected
Brownian motion, particle collisions, Wishart process, radial Dunkl process, Weyl
chamber.