On Positive Recurrence of Constrained Diffusion Processes

By Rami Atar, Amarjit Budhiraja and Paul Dupuis Technion-Israel Institute of Technology, University of North Carolina at Chapel Hill and Brown University Let G ⊂ IRk be a convex polyhedral cone with vertex at the origin given as the intersection of half spaces {Gi, i = 1, · · · , N}, where ni and di denote the inward normal and direction of constraint associated with Gi, respectively. Stability properties of a class of diffusion processes, constrained to take values in G, are studied under the assumption that the Skorokhod problem defined by the data {(ni, di), i = 1, · · · , N} is well posed and the Skorokhod map is Lipschitz continuous. Explicit conditions on the drift coefficient, b(·), of the diffusion process are given under which the constrained process is positive recurrent and has a unique invariant measure. Define