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Strong ergodicity for continuous-time, non-homogeneous Markov chains

Published online by Cambridge University Press:  14 July 2016

Mark Scott ,
Barry C. Arnold  and
Dean L. Isaacson
Mark Scott*
Affiliation:
Mayo Clinic
Barry C. Arnold*
Affiliation:
University of California, Riverside
Dean L. Isaacson*
Affiliation:
Iowa State University
*
∗Postal address: Department of Oncology, Mayo Clinic, Rochester, MN 55901, U.S.A.
∗∗Postal address: Department of Statistics, University of California, Riverside, CA 92501, U.S.A.
∗∗∗Postal address: Department of Statistics, Iowa State University, Ames, IA 50011, U.S.A.
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Abstract

Characterizations of strong ergodicity for Markov chains using mean visit times have been found by several authors (Huang and Isaacson (1977), Isaacson and Arnold (1978)). In this paper a characterization of uniform strong ergodicity for a continuous-time non-homogeneous Markov chain is given. This extends the characterization, using mean visit times, that was given by Isaacson and Arnold.

Keywords

MARKOV CHAINNON-HOMOGENEOUSCONTINUOUS TIMESTRONG ERGODICITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 692 - 694
Copyright
Copyright © Applied Probability Trust 1982 

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References

Huang, C. and Isaacson, D. (1977) Ergodicity using mean visit times. J. London Math. Soc. 14, 570–576.Google Scholar
Isaacson, D. and Arnold, B. (1978) Strong ergodicity for continuous-time Markov chains. J. Appl. Prob. 15, 699–706.CrossRefGoogle Scholar
Scott, M. (1979) Characterizations of Strong Ergodicity for Continuous-Time Markov Chains. Ph.D. dissertation, Iowa State University, Ames, Iowa.CrossRefGoogle Scholar