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A note on the ergodicity of Markov chains

Published online by Cambridge University Press:  14 July 2016

Zvi Rosberg
Zvi Rosberg*
Affiliation:
Technion–Israel Institute of Technology
*
∗Postal address: Department of Computer Science, Technion, Technion City, Haifa 32000, Israel. This research was mainly done while the author was visiting C.O.R.E., Université de Louvain, and was completed at the University of Illinois.
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Abstract

For an aperiodic, irreducible Markov chain with the non-negative integers as state space, a criterion for ergodicity is given. This criterion generalizes the criteria appearing in Foster (1953), Pakes (1969) and Marlin (1973), in the sense that any test function (Liapunov function) which satisfies their conditions also satisfies ours. Applications are presented through some examples.

Keywords

ERGODICITYMARKOV CHAINLEFT-CONTINUOUS CHAINSRIGHT-CONTINUOUS CHAINSRENEWAL CHAINS
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 112 - 121
Copyright
Copyright © Applied Probability Trust 

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References

Foster, F. G. (1953) On the stochastic matrices associated with certain queueing processes. Ann. Math. Statist. 24, 355–360.Google Scholar
Kemeny, J. G., Snell, J. L. and Knapp, A. W. (1976) Denumerable Markov Chains. Springer-Verlag, New York.CrossRefGoogle Scholar
Marlin, P. G. (1973) On the ergodic theory of Markov chains. Operat. Res. 21, 617–622.Google Scholar
Pakes, A. G. (1969) Some conditions of ergodicity and recurrence of Markov chains. Operat. Res. 17, 1058–1061.Google Scholar