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On transient regenerative processes

Published online by Cambridge University Press:  14 July 2016

Emily Murphree  and
Walter L. Smith
Emily Murphree*
Affiliation:
Miami University
Walter L. Smith*
Affiliation:
University of North Carolina
*
∗Postal address: Department of Mathematics and Statistics, Miami University, Bachelor Hall, Oxford, OH 45056, USA.
∗∗Postal address: Department of Statistics, University of North Carolina, Chapel Hill, NC 27514, USA.
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Abstract

A transient cumulative process based upon a sequence of possibly infinite lifetimes is defined, and examples of such a process are described. Given a mild condition on the improper lifetime distribution and given that all lifetimes observed by time t are finite, the expected value of this transient process at t is related to the expected value of a cumulative process based upon proper lifetimes. This relationship is exploited to show that the conditional behavior of the transient process is analogous to that of a proper process and, in particular, the transient process is asymptotically normal.

Keywords

CUMULATIVE PROCESSESRENEWALSNORMAL LIMIT LAWS
Type
Research Papers
Information
Journal of Applied Probability , Volume 23 , Issue 1 , March 1986 , pp. 52 - 70
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

Research supported by the Office of Naval Research under grant N00014–76-C0550.

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