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On non-singular Markov renewal processes with an application to a growth–catastrophe model

Published online by Cambridge University Press:  14 July 2016

Seppo Niemi
Seppo Niemi*
Affiliation:
University of Helsinki
*
∗Postal address: Department of Mathematics, University of Helsinki, Hallituskatu 15, 00100 Helsinki 10, Finland.
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Abstract

The paper is concerned with Markov renewal processes satisfying a certain non-singularity condition. The relation of this condition to irreducibility, Harris recurrence and regularity of the associated forward Markov process is studied. This enables one to prove limit theorems of a total variation type for Markov renewal processes and semi-regenerative processes by applying Orey's theorem to the forward process. The results are applied to a GI/G/1 queue and a growth-catastrophe population model.

Keywords

SEMI-REGENERATIVE PROCESSESLIMIT THEOREMSNON-SINGULARITYPOPULATION MODELS
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 253 - 266
Copyright
Copyright © Applied Probability Trust 1985 

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