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An example on geometric ergodicity of a finite Markov chain

Published online by Cambridge University Press:  14 July 2016

Jozef L. Teugels
Jozef L. Teugels*
Affiliation:
Catholic University of Louvain, Belgium
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Abstract

A discrete time Markov chain with (n + 1) states is constructed in which there are n states having different decay parameters for geometric ergodicity.

Keywords

MARKOV CHAINSTOCHASTIC MATRIXDOUBLY STOCHASTICFINITE CHAINEIGENVALUEGEOMETRIC ERGODICITYDECAY PARAMETER

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 466 - 469
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Gantmacher, F. R. (1958) Matrizenrechnung. VEB Deutscher Verlag Wiss., Berlin.Google Scholar
[2] Kendall, D. G. (1959) Unitary dilations of Markov transition operators and the corresponding integral representations for transition-probability matrices. Probability and Statistics. Ed. by Grenander, U. Wiley, New York. 139–161.Google Scholar
[3] Vere-Jones, D. (1962) Geometric ergodicity in denumerable Markov chains. Quart. J. Math. 13, 7–28.CrossRefGoogle Scholar