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On the equivalence of certain Markov chains

Published online by Cambridge University Press:  14 July 2016

Pedro Vit
Pedro Vit*
Affiliation:
CIMAS, Universidad Nacional Autónoma de México
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Abstract

It is shown that an irreducible and aperiodic Markov chain can be altered preserving irreducibility without altering the nature of the chain in the sense that, the modified chain is transient (recurrent) if and only if the original chain is transient (recurrent). Furthermore, it is shown by means of a counterexample that ergodicity (null-recurrence) is not preserved.

An interesting application of this result is a simple proof of Pakes's generalization of Foster's criterion for a chain to be recurrent.

Keywords

EQUIVALENT MARKOV CHAINSFOSTER'S CRITERION FOR RECURRENCEPAKES'S CRITERION FOR RECURRENCETRANSFORMATION OF MARKOV CHAINS
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 2 , June 1976 , pp. 357 - 360
Copyright
Copyright © Applied Probability Trust 1976 

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References

Foster, F. G. (1953) On the stochastic matrices associated with certain queuing processes. Ann. Math. Statist. 24, 355–360.Google Scholar
Pakes, A. G. (1969) Some conditions for ergodicity and recurrence of Markov chains Operat. Res. 17, 1058–1061.Google Scholar