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Semi-Markov Replacement Chains

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Ioannis I. Gerontidis
Ioannis I. Gerontidis*
Affiliation:
University of Thessaloniki
*
* Postal address: Mathematics Department, University of Thessaloniki, 54006 Thessaloniki, Greece.
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Abstract

We consider an absorbing semi-Markov chain for which each time absorption occurs there is a resetting of the chain according to some initial (replacement) distribution. The new process is a semi-Markov replacement chain and we study its properties in terms of those of the imbedded Markov replacement chain. A time-dependent version of the model is also defined and analysed asymptotically for two types of environmental behaviour, i.e. either convergent or cyclic. The results contribute to the control theory of semi-Markov chains and extend in a natural manner a wide variety of applied probability models. An application to the modelling of populations with semi-Markovian replacements is also presented.

Keywords

COMPENSATIONCONTROL OF SEMI-MARKOV CHAINSNON-STATIONARITYQUASI-PERIODICITYSTOCHASTIC POPULATION MODELSUNIFORM STRONG ERGODICITY

MSC classification

Primary: 60K15: Markov renewal processes, semi-Markov processes
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 3 , September 1994 , pp. 728 - 755
Copyright
Copyright © Applied Probability Trust 1994 

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