On transient regenerative processes-Reference-Cited by-同舟云学术

On transient regenerative processes

Published:1986-03 Issue:1 Volume:23 Page:52-70
ISSN:0021-9002
Container-title:Journal of Applied Probability
language:en
Short-container-title:Journal of Applied Probability

Author:

Murphree Emily,Smith Walter L.

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.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference12 articles.

1. A Theorem on Sums of Independent Positive Random Variables and Its Applications to Branching Random Processes

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