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Renewal-type behavior of absorption times in Markov chains

Part of: Special processes Combinatorics

Published online by Cambridge University Press:  01 July 2016

Bernard Van Cutsem  and
Bernard Ycart
Bernard Van Cutsem*
Affiliation:
Institut IMAG
Bernard Ycart*
Affiliation:
Institut IMAG
*
* Postal address: LMC/IMAG B.P. 53, 38041 Grenoble Cedex 9, France, e-mail: ycart@imag.fr
* Postal address: LMC/IMAG B.P. 53, 38041 Grenoble Cedex 9, France, e-mail: ycart@imag.fr
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Abstract

This paper studies the absorption time of an integer-valued Markov chain with a lower-triangular transition matrix. The main results concern the asymptotic behavior of the absorption time when the starting point tends to infinity (asymptotics of moments and central limit theorem). They are obtained using stochastic comparison for Markov chains and the classical theorems of renewal theory. Applications to the description of large random chains of partitions and large random ordered partitions are given.

Keywords

RENEWAL PROCESSESRANDOM CHAINS OF PARTITIONSRANDOM ORDERED PARTITIONS

MSC classification

Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Secondary: 05A: Enumerative combinatorics
Type
Research Article
Information
Advances in Applied Probability , Volume 26 , Issue 4 , December 1994 , pp. 988 - 1005
Copyright
Copyright © Applied Probability Trust 1994 

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