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Limit theorems for α-recurrent semi-Markov processes

Published online by Cambridge University Press:  01 July 2016

Esa Nummelin
Esa Nummelin*
Affiliation:
Institute of Mathematics, Helsinki University of Technology
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Abstract

In this paper the limit behaviour of α-recurrent Markov renewal processes and semi-Markov processes is studied by using the recent results on the concept of α-recurrence for Markov renewal processes. Section 1 contains the preliminary results, which are needed later in the paper. In Section 2 we consider the limit behaviour of the transition probabilities Pij(t) of an α-recurrent semi-Markov process. Section 4 deals with quasi-stationarity. Our results extend the results of Cheong (1968), (1970) and of Flaspohler and Holmes (1972) to the case in which the functions to be considered are directly Riemann integrable. We also try to correct the errors we have found in these papers. As a special case from our results we consider continuous-time Markov processes in Sections 3 and 5.

Keywords

MARKOV RENEWAL PROCESSESSEMI-MARKOV PROCESSESα-RECURRENCEQUASISTATIONARITYSEMI-MARKOV KERNELMARKOV PROCESSESQ-MATRIX
Type
Research Article
Information
Advances in Applied Probability , Volume 8 , Issue 3 , September 1976 , pp. 531 - 547
Copyright
Copyright © Applied Probability Trust 1976 

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References

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