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

1 December 1977

journal article
Published by Cambridge University Press (CUP) in Journal of Applied Probability

Vol. 14 (4) , 740-747
https://doi.org/10.2307/3213347

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

This publication has 4 references indexed in Scilit:

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