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An invariance principle for semi-Markov processes

Published online by Cambridge University Press:  01 July 2016

D. McDonald
D. McDonald*
Affiliation:
University of Ottawa
*
∗Postal address: Department of Mathematics, University of Ottawa, Ottawa, Ontario, Canada KIN 9B4.
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Abstract

Let (I(t))∞t = () be a semi-Markov process with state space II and recurrent probability transition kernel P. Subject to certain mixing conditions, where Δis an invariant probability measure for P and μb is the expected sojourn time in state b ϵΠ. We show that this limit is robust; that is, for each state b ϵ Πthe sojourn-time distribution may change for each transition, but, as long as the expected sojourn time in b is µb on the average, the above limit still holds. The kernel P may also vary for each transition as long as Δis invariant.

Keywords

LIMITSNON-STATIONARYSEMI-REGENERATIVE
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 1 , March 1985 , pp. 100 - 126
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Research supported by the National Research Council of Canada.

References

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