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Return times in nearly-completely decomposable stochastic processes

Published online by Cambridge University Press:  14 July 2016

G. Latouche  and
G. Louchard
G. Latouche
Affiliation:
Université Libre de Bruxelles
G. Louchard
Affiliation:
Université Libre de Bruxelles
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Abstract

Consider a finite irreducible aperiodic Markov chain with nearly-completely decomposable stochastic matrix: i.e. a Markov chain for which the states can be grouped into disjoint aggregates, in such a way that the probabilities of transition between states of the same aggregate are large compared to the probabilities of transition between states belonging to different aggregates. Let Ω be a subset of one of the aggregates. Second-order approximations are determined for the first and second moments of the time to reach Ω and the return time to Ω.

Keywords

MARKOV CHAINNEARLY-COMPLETE DECOMPOSABILITYRETURN TIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 2 , June 1978 , pp. 251 - 267
Copyright
Copyright © Applied Probability Trust 1978 

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References

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