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General solidarity theorems for semi-Markov processes

Published online by Cambridge University Press:  14 July 2016

Choong K. Cheong  and
Jozef L. Teugels
Choong K. Cheong*
Affiliation:
Catholic University of Louvain, Belgium
Jozef L. Teugels
Affiliation:
Catholic University of Louvain, Belgium
*
*Now at the University of Malaya, Kuala Lumpur.
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Abstract

Let {Zt, t ≧ 0} be an irreducible regular semi-Markov process with transition probabilities Pij (t). Let f(t) be non-negative and non-decreasing to infinity, and let λ ≧ 0. This paper identifies a large set of functions f(t) with the solidarity property that convergence of the integral ≧ eλtf(t)Pij(t) dt for a specific pair of states i and j implies convergence of the integral for all pairs of states. Similar results are derived for the Markov renewal functions Mij (t). Among others it is shown that f(t) can be taken regularly varying.

Keywords

SEMI-MARKOV PROCESSMARKOV RENEWAL PROCESSSOLIDARITY PROPERTYCLASS PROPERTYREGULAR VARIATIONSLOWLY VARYING FUNCTIONLIMIT THEOREMSGEOMETRIC ERGODICITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 4 , December 1972 , pp. 789 - 802
Copyright
Copyright © Applied Probability Trust 1972 

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References

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