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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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