Abstract
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.
Citation
Hong Chen. "A sufficient condition for the positive recurrence of a semimartingale reflecting Brownian motion in an orthant." Ann. Appl. Probab. 6 (3) 758 - 765, August 1996. https://doi.org/10.1214/aoap/1034968226
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