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Foster-type criteria for Markov chains on general spaces

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Brian H. Fralix
Brian H. Fralix*
Affiliation:
Georgia Institute of Technology
*
∗Postal address: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA. Email address: bfralix@isye.gatech.edu
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Abstract

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This paper establishes new Foster-type criteria for a Markov chain on a general state space to be Harris recurrent, positive Harris recurrent, or geometrically ergodic. The criteria are based on drift conditions involving stopping times rather than deterministic steps. Meyn and Tweedie (1994) developed similar criteria involving random-sized steps, independent of the Markov chain under study. They also posed an open problem of finding criteria involving stopping times. Our results essentially solve that problem. We also show that the assumption of ψ-irreducibility is not needed when stating our drift conditions for positive Harris recurrence or geometric ergodicity.

Keywords

Markov chainFoster's criterionHarris recurrencegeometric ergodicitydrift criterion

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Short Communications
Information
Journal of Applied Probability , Volume 43 , Issue 4 , December 2006 , pp. 1194 - 1200
Copyright
© Applied Probability Trust 2006 

References

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