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Transient renewal processes in the subexponential case

Published online by Cambridge University Press:  14 July 2016

Emily S. Murphree
Emily S. Murphree*
Affiliation:
Miami University
*
∗Postal address: Department of Mathematics and Statistics, Miami University, Bachelor Hall, Oxford, OH 45056, USA.
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Abstract

A transient renewal process based on a sequence of possibly infinite waiting times is defined. The process is studied when the (rescaled) distribution of the waiting times belongs to the subexponential class of distributions. In this case, even conditional on all waiting times observed by time t being finite, the distributions of the forward and backward delays at t are asymptotically degenerate. Also, the conditional moments of the number of events by time t converge to the same finite limits as the unconditional moments.

Keywords

FORWARD DELAYBACKWARD DELAY
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 88 - 96
Copyright
Copyright © Applied Probability Trust 1987 

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