Open Access
Translator Disclaimer
April 1996 A Liapounov bound for solutions of the Poisson equation
Peter W. Glynn, Sean P. Meyn
Ann. Probab. 24(2): 916-931 (April 1996). DOI: 10.1214/aop/1039639370


In this paper we consider $\psi$-irreducible Markov processes evolving in discrete or continuous time on a general state space. We develop a Liapounov function criterion that permits one to obtain explicit bounds on the solution to the Poisson equation and, in particular, obtain conditions under which the solution is square integrable.

These results are applied to obtain sufficient conditions that guarantee the validity of a functional central limit theorem for the Markov process. As a second consequence of the bounds obtained, a perturbation theory for Markov processes is developed which gives conditions under which both the solution to the Poisson equation and the invariant probability for the process are continuous functions of its transition kernel. The techniques are illustrated with applications to queueing theory and autoregressive processes.


Download Citation

Peter W. Glynn. Sean P. Meyn. "A Liapounov bound for solutions of the Poisson equation." Ann. Probab. 24 (2) 916 - 931, April 1996.


Published: April 1996
First available in Project Euclid: 11 December 2002

zbMATH: 0863.60063
MathSciNet: MR1404536
Digital Object Identifier: 10.1214/aop/1039639370

Primary: 60J10 , 68M20

Keywords: Foster's criterion , functional central limit theorem , Liapounov function , Markov chain , Markov process , Perturbation theory , Poisson equation

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.24 • No. 2 • April 1996
Back to Top