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Necessary and sufficient conditions for recurrence and transience of Markov chains, in terms of inequalities

Published online by Cambridge University Press:  14 July 2016

Jean-François Mertens ,
Ester Samuel-Cahn  and
Shmuel Zamir
Jean-François Mertens
Affiliation:
Université de Louvain
Ester Samuel-Cahn
Affiliation:
Hebrew University of Jerusalem
Shmuel Zamir
Affiliation:
Hebrew University of Jerusalem
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Abstract

For an aperiodic, irreducible Markov chain with the non-negative integers as state space it is shown that the existence of a solution to in which yi → ∞is necessary and sufficient for recurrence, and the existence of a bounded solution to the same inequalities, with yk < yo, · · ·, yN–1 for some k ≧ N, is necessary and sufficient for transience.

Keywords

RECURRENCETRANSIENCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 4 , December 1978 , pp. 848 - 851
Copyright
Copyright © Applied Probability Trust 1978 

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References

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