Periodicity in Markov renewal theory

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 comple...

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Bibliographic Details
Published in:Advances in applied probability 1974-03, Vol.6 (1), p.61-78
Main Author: Çinlar, Erhan
Format: Article
Language:English
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Summary: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.
ISSN:0001-8678
1475-6064
DOI:10.1017/S0001867800039719