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Waiting times without memory

Published online by Cambridge University Press:  14 July 2016

Richard T. Durrett  and
S. G. Ghurye
Richard T. Durrett
Affiliation:
Stanford University
S. G. Ghurye
Affiliation:
University of Alberta
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Abstract

A waiting time without memory, or age-independent residual life-time, is a positive-valued random variable T with the property that for any x, y > 0, given that T >x, the conditional probability of T >x +y is the same as the unconditional probability of T >y; in other words, the physical process operates as if it has no memory concerning the successive occurrences of a certain event. The paper investigates the consequences of defining the property of lack of memory on more general time-domains than the positive reals. As a side issue, there is discussion of a stochastic variation of Cauchy's functional equation.

Keywords

WAITING TIMESRESIDUAL LIFE-TIMESLACK OF MEMORYCAUCHY FUNCTIONAL EQUATIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 65 - 75
Copyright
Copyright © Applied Probability Trust 1976 

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