Annals of Probability

Lyapunov Functions for Semimartingale Reflecting Brownian Motions

Paul Dupuis and Ruth J. Williams

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Probab., Volume 22, Number 2 (1994), 680-702.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988725

Digital Object Identifier
doi:10.1214/aop/1176988725

Mathematical Reviews number (MathSciNet)
MR1288127

Zentralblatt MATH identifier
0808.60068

JSTOR
links.jstor.org

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60J65: Brownian motion [See also 58J65] 60K25: Queueing theory [See also 68M20, 90B22] 34D20: Stability

Keywords
Recurrence Lyapunov functions semimartingale reflecting Brownian motions Skorokhod problem dynamical system optimal control

Citation

Dupuis, Paul; Williams, Ruth J. Lyapunov Functions for Semimartingale Reflecting Brownian Motions. Ann. Probab. 22 (1994), no. 2, 680--702. doi:10.1214/aop/1176988725. https://projecteuclid.org/euclid.aop/1176988725


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