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A note on the existence of regeneration times

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Karl Sigman ,
Hermann Thorisson  and
Ronald W. Wolff
Karl Sigman*
Affiliation:
Columbia University
Hermann Thorisson*
Affiliation:
University of Iceland
Ronald W. Wolff*
Affiliation:
University of California at Berkeley
*
∗Postal address: Department of Industrial Engineering and Operations Research, Columbia University, Mudd Building NY, NY 10027–6699, USA., e-mail: sigman@ieor.columbia.edu
∗∗Postal address: Science Institute-University of Iceland, Dunhaga 3, 107 Reykjavik, Iceland. e-mail: thoris@rhi.hi.is
∗∗∗Postal address: Department of Industrial Engineering and Operations Research, University of California at Berkeley, Etcheverry Hall, Berkeley, CA 94720, USA.
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Abstract

We rigorously prove that for a stochastic process, , the existence of a first regeneration time, R1, implies the existence of an infinite sequence of such times, {R1, R2, · ·· }, and hence that the definition of regenerative process need only demand the existence of a first regeneration time. Here we include very general processes up to and including processes where cycles are stationary but not necessarily independent and identically distributed.

Keywords

REGENERATIVE PROCESSCYCLES

MSC classification

Primary: 60K05: Renewal theory
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 1116 - 1122
Copyright
Copyright © Applied Probability Trust 1994 

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