Boundary behavior of a constrained Brownian motion between reflecting-repellent walls

Details Boundary behavior of a constrained Brownian motion between reflecting-repellent walls Boundary behavior of a constrained Brownian motion between reflecting-repellent walls

2009-10-09

arxiv.org/abs/0910.1820v1

Probability and Mathematical Statistics 30, 2 (2010) 273-287

Mathematics

Probability

Scientific paper

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 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 case. A complete answer to the question of attainability of the walls of the Weyl chamber may be given for a radial Dunkl process.

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