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Algebraic characterization of infinite Markov chains where movement to the right is limited to one step

Published online by Cambridge University Press:  14 July 2016

Ester Samuel-Cahn  and
Shmuel Zamir
Ester Samuel-Cahn
Affiliation:
The Hebrew University of Jerusalem
Shmuel Zamir
Affiliation:
The Hebrew University of Jerusalem
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Abstract

We consider an infinite Markov chain with states E0, E1, …, such that E1, E2, … is not closed, and for i ≧ 1 movement to the right is limited by one step. Simple algebraic characterizations are given for persistency of all states, and, if E0 is absorbing, simple expressions are given for the probabilities of staying forever among the transient states. Examples are furnished, and simple necessary conditions and sufficient conditions for the above characterizations are given.

Keywords

ALGEBRAIC CHARACTERIZATION OF MARKOV CHAINSPERSISTENCYABSORPTION PROBABILITIES
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 4 , December 1977 , pp. 740 - 747
Copyright
Copyright © Applied Probability Trust 1977 

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References

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