Hostname: page-component-7dd5485656-7jgsp Total loading time: 0 Render date: 2025-10-31T07:33:30.943Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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