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

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.

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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

Information

Published: August 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0860.60062
MathSciNet: MR1410114
Digital Object Identifier: 10.1214/aoap/1034968226

Subjects:
Primary: 60J60
Secondary: 34D20 , 60J65 , 60K25

Keywords: fluid network , linear Lyapunov function , positive recurrence , Semimartingale reflecting Brownian motion on an orthant , stationary distribution

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.6 • No. 3 • August 1996
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