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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

Information

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

[1] Courtois, P. J. and Louchard, G. (1976) Approximation of eigencharacteristics in nearly-completely decomposable stochastic systems. Stoch. Proc. Appl. 4, 283–296.CrossRefGoogle Scholar
[2] Kato, T. (1966) Perturbation Theory for Linear Operators. Springer-Verlag, Berlin.Google Scholar
[3] Latouche, G. and Louchard, G. (1977) Return times in nearly-completely decomposable stochastic processes. Report No. 45, Laboratoire d'informatique Théorique, Université Libre de Bruxelles.Google Scholar
[4] Louchard, G. (1966) Recurrence times and capacities in finite ergodic chains. Duke Math. J. 33, 13–22.CrossRefGoogle Scholar
[5] Simon, H. A. and Ando, A. (1961) Aggregation of variables in dynamic systems. Econometrics 29, 111–138.Google Scholar