Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-08T02:58:39.675Z Has data issue: false hasContentIssue false

A Lyapunov Criterion for Invariant Probabilities with Geometric Tail

Published online by Cambridge University Press:  27 July 2009

Jean B. Lasserre
Affiliation:
7 Avenue du Colonel Roche, 31077 Toulouse Cédex 4, France

Abstract

Given a Markov chain on a countable state space, we present a Lyapunov (sufficient) condition for existence of an invariant probability with a geometric tail.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Hernández-Lerma, O. & Lasserre, J.B. (1995). Invariant probabilities for Feller Markov chains. Journal of Applied Mathematics and Stochastic Analysis 8: 341345.CrossRefGoogle Scholar
2.Lasserre, J.B. (1997). Invariant probabilities for Markov chains on a metric space. Statistics and Probability Letters 34: 259265.CrossRefGoogle Scholar
3.Lasserre, J.B. & Tijms, H. (1996). Invariant probabilities with geometric tail. Probability in the Engineering and Informational Sciences 10: 213221.CrossRefGoogle Scholar
4.Malyshev, V.A. & Menshikov, M.V. (1981). Ergodicity, continuity and analyticity of countable Markov chains. Transactions of the Moscow Mathematics Society 1: 148.Google Scholar
5.Royden, H.L. (1988). Real analysis. New York: Macmillan.Google Scholar
6.Spieksma, F.M. & Tweedie, R.L. (1994). Strengthening ergodicity to geometric ergodicity of Markov chains. Stochastic Models 10: 4575.CrossRefGoogle Scholar
7.Takahashi, Y. (1981). Asymptotic exponentiality of the tail of the waiting time distribution in a Ph/Ph/c queue. Advances in Applied Probability 13: 619630.CrossRefGoogle Scholar
8.Tijms, H.C. (1994). Stochastic models: An algorithmic approach. Chichester: John Wiley & Sons Ltd.Google Scholar