  Let G \subset \R^k be a convex polyhedral cone with vertex at the origin
given as the intersection of half spaces {G_i, i= 1, ..., N}, where n_i and d_i
denote the inward normal and direction of constraint associated with G_i,
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 {(n_i, d_i), i = 1, ..., N} is well posed
and the Skorokhod map is Lipschitz continuous. Explicit conditions on the drift
coefficient, b(\cdot), of the diffusion process are given under which the
constrained process is positive recurrent and has a unique invariant measure.
Define \C \Df{- \sum_{i=1}^N \alpha_i d_i; \alpha_i \ge 0, i \in \{1, ..., N}}.
Then the key condition for stability is that there exists \delta \in (0,
\infty) and a bounded subset A of G such that for all x \in G\backslash A, b(x)
\in \C and \dist(b(x), \partial \C) \ge \delta, where \partial \C denotes the
boundary of \C.
