Open Access
April, 1994 Lyapunov Functions for Semimartingale Reflecting Brownian Motions
Paul Dupuis, Ruth J. Williams
Ann. Probab. 22(2): 680-702 (April, 1994). DOI: 10.1214/aop/1176988725


We prove that a sufficient condition for a semimartingale reflecting Brownian motion in an orthant (SRBM) to be positive recurrent is that all solutions of an associated deterministic Skorokhod problem are attracted to the origin. To prove this result, we construct a Lyapunov function for the SRBM.


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Paul Dupuis. Ruth J. Williams. "Lyapunov Functions for Semimartingale Reflecting Brownian Motions." Ann. Probab. 22 (2) 680 - 702, April, 1994.


Published: April, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0808.60068
MathSciNet: MR1288127
Digital Object Identifier: 10.1214/aop/1176988725

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

Keywords: dynamical system , Lyapunov functions , optimal control , recurrence , semimartingale reflecting Brownian motions , Skorokhod problem

Rights: Copyright © 1994 Institute of Mathematical Statistics

Vol.22 • No. 2 • April, 1994
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