A SUFFICIENT CONDITION FOR THE POSITIVE RECURRENCE OF A SEMIMARTINGALE REFLECTING BROWNIAN MOTION IN AN ORTHANT
成果类型：
Article
署名作者：
Chen, Hong
署名单位：
University of British Columbia
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1996
页码：
758-765
关键词：
摘要：
Dupuis and Williams proved that a sufficient condition for the positive recurrence and the existence of a unique stationary distribution for a semimartingale reflecting Brownian motion in an orthant (SRBM) is that all solutions of an associated deterministic Skorohod problem are attracted to the origin. In this paper, we derive a sufficient condition under which we can construct an explicit linear Lyapunov function for the Skorohod problem. Thus, this implies a sufficient condition for the stability of the deterministic Skorohod problem. The existence of such a linear Lyapunov function is equivalent to the feasibility of a set of linear inequalities. In the two-dimensional case, we recover the necessary and sufficient conditions for the positive recurrence. Some explicit sufficient conditions are derived for the higher-dimensional case.