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Renewal processes decomposable into i.i.d. components

Published online by Cambridge University Press:  01 July 2016

Yoshifusa Ito*
Affiliation:
Nagoya University

Abstract

Let N be a stationary renewal process with a probability density function f(t). Suppose that N can be expressed as the superposition of a finite number of i.i.d. stationary components N(1), …, N(p) (p≧2). Then, under a supplementary condition on f(t), N and N(1), …, N(p) are all Poisson. This is proved by using recurrence relations given in Ito (1978) for the probability distribution of i.i.d. components of a superposition process.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1980 

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References

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