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Criteria for strong ergodicity of Markov chains

Published online by Cambridge University Press:  14 July 2016

Dean Isaacson  and
Richard L. Tweedie
Dean Isaacson
Affiliation:
Iowa State University
Richard L. Tweedie
Affiliation:
Division of Mathematics and Statistics, C.S.I.R.O., Canberra
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Abstract

For finite Markov chains, the concepts of ergodicity and strong ergodicity are equivalent, but this is not necessarily the case when the state space is infinite. In this note we give some new characterizations of strong ergodicity. These lead to simple necessary or sufficient criteria for strong ergodicity, which readily enable us to classify a number of examples.

Keywords

HITTING TIMESSTRONG ERGODICITYMARKOV CHAINSRANDOM WALKRENEWAL CHAINSRIGHT-CONTINUOUS CHAINSSKIP-FREE CHAINS
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 1 , March 1978 , pp. 87 - 95
Copyright
Copyright © Applied Probability Trust 1978 

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References

Dobrushin, R. L. (1956) Central limit theorem for nonstationary Markov chains, Theory Prob. Appl. 1, 65–80, 329–383.Google Scholar
Feller, W. (1968) An Introduction to Probability Theory and its Applications, Vol. 1, 3rd edn. Wiley, New York.Google Scholar
Foster, F. G. (1953) On the stochastic matrices associated with certain queueing processes. Ann. Math. Statist. 24, 355–360.Google Scholar
Griffeath, D. (1975) Uniform coupling of nonhomogeneous Markov chains. J. Appl. Prob. 12, 753–762.Google Scholar
Huang, C. and Isaacson, D. (1976) Ergodicity using mean visit times. J. London Math. Soc. 14, 570–576.Google Scholar
Isaacson, D. and Luecke, G. (1976) Ergodicity versus strong ergodicity, Stoch. Proc. Appl. To appear.Google Scholar
Miller, H. D. (1966) Geometric ergodicity in a class of denumerable Markov chains. Z. Wahrscheinlichkeitsth. 4, 354–373.Google Scholar
Nummelin, E. (1978) A splitting technique for f-recurrent Markov chains, Z. Wahrscheinlichteitsth. To appear.Google Scholar
Samuel-Cahn, E. and Zamir, S. (1977) Algebraic characterization of infinite Markov chains where movement to the right is limited to one step. J. Appl. Prob. 14, 740–747.CrossRefGoogle Scholar
Tweedie, R. L. (1975) The robustness of positive recurrence and recurrence of Markov chains. J. Appl. Prob. 12, 744–752.Google Scholar
Tweedie, R. L. (1976) Criteria for classifying general Markov chains. Adv. Appl. Prob. 8, 737–771.Google Scholar
Tweedie, R. L. (1977) Hitting times of Markov chains, with application to state-dependent queues. Bull. Austral. Math. Soc. 17, 97–107.CrossRefGoogle Scholar