On Positive Recurrence of Constrained Diffusion Processes

Details On Positive Recurrence of Constrained Diffusion Processes On Positive Recurrence of Constrained Diffusion Processes

2005-01-02

arxiv.org/abs/math/0501018v1

The Annals of Probability, Vol. 29, No. 2, 979-1000 (2001)

Mathematics

Probability

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On Positive Recurrence of Constrained Diffusion Processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Positive Recurrence of Constrained Diffusion Processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Positive Recurrence of Constrained Diffusion Processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-557059