Necessary and sufficient conditions for recurrence and transience of Markov chains, in terms of inequalities
Authors:
- Jean-François MertensJMJean-François Mertens
- Ester Samuel-CahnESEster Samuel-Cahn
- Shmuel ZamirSZShmuel Zamir
- 1 December 1978
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 15 (4) , 848-851
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
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This publication has 3 references indexed in Scilit:
- A Note on Feedback Queues with Bulk ServiceJournal of the ACM, 1972
- Some Conditions for Ergodicity and Recurrence of Markov ChainsOperations Research, 1969
- On the Stochastic Matrices Associated with Certain Queuing ProcessesThe Annals of Mathematical Statistics, 1953