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Renewal theory in a random environment

Published online by Cambridge University Press:  24 October 2008

Laurence A. Baxter  and
Linxiong Li
Laurence A. Baxter
Affiliation:
Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794, USA
Linxiong Li
Affiliation:
Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794, USA
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Abstract

A random environment is modelled by an arbitrary stochastic process, the future of which is described by a σ-algebra. Renewal processes and alternating renewal processes are defined in this environment by considering the conditional distributions of random variables generated by the processes with respect to the σ-algebra. Generalizations of several of the standard limit theorems of renewal theory are derived.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 1 , July 1994 , pp. 179 - 190
Copyright
Copyright © Cambridge Philosophical Society 1994

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