Algebraic characterization of infinite Markov chains where movement to the right is limited to one step
1977 ◽
Vol 14
(04)
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pp. 740-747
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Keyword(s):
One Step
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We consider an infinite Markov chain with states E 0, E 1, …, such that E 1, E 2, … 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 E 0 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.