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Periodicity in Markov renewal theory

Published online by Cambridge University Press:  01 July 2016

Erhan Çinlar
Erhan Çinlar*
Affiliation:
Northwestern University, Evanston, Illinois
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Abstract

In an irreducible Markov renewal process either all states are periodic or none are. In the former case they all have the same period. Periodicity and the period can be determined by direct inspection from the semi-Markov kernel defining the process. The periodicity considerably increases the complexity of the limits in Markov renewal theory especially for transient initial states. Two Markov renewal limit theorems will be given with particular attention to the roles of periodicity and transient states. The results are applied to semi-Markov and semi-regenerative processes.

Keywords

MARKOV RENEWAL THEORYLIMIT THEOREMSPERIODICITYSEMI-REGENERATIVE AND SEMI-MARKOV PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 1 , March 1974 , pp. 61 - 78
Copyright
Copyright © Applied Probability Trust 1974 

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References

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