Necessary and sufficient conditions for recurrence and transience of Markov chains, in terms of inequalities-Reference-Cited by-同舟云学术

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

Published:1978-12 Issue:4 Volume:15 Page:848-851
ISSN:0021-9002
Container-title:Journal of Applied Probability
language:en
Short-container-title:Journal of Applied Probability

Author:

Mertens Jean-François,Samuel-Cahn Ester,Zamir Shmuel

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.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference5 articles.

1. On the Stochastic Matrices Associated with Certain Queuing Processes

2. A Note on Feedback Queues with Bulk Service

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