On positive recurrence of constrained diffusion processes

• 成果类型: Article
• 署名作者: Atar, R; Budhiraja, A; Dupuis, P
• 署名单位: Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill; Brown University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1008956699
• 发表日期: 2001
• 页码: 979-1000
• 关键词: reflecting brownian-motion; networks

摘要

Let G subset of 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((.)), of the diffusion process are given under which the constrained process is positive recurrent and has a unique invariant measure. Define l (=) over circle{-Sigma (N)(i=1) alpha (i) d(i) ; alpha (i) greater than or equal to 0, i is an element of {1,..., N} } Then the key condition for stability is that there exists delta is an element of (0,infinity) and a bounded subset A of G such that for all x is an element of G\A, b(x) is an element of l and dist(b(x), partial derivativel) greater than or equal to delta, where partial derivativel denotes the boundary of l .