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Renewal processes decomposable into i.i.d. components

Published online by Cambridge University Press:  01 July 2016

Yoshifusa Ito
Yoshifusa Ito*
Affiliation:
Nagoya University
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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.

Keywords

POINT PROCESSRENEWAL PROCESSPOISSON PROCESSDECOMPOSITION OF POINT PROCESS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 3 , September 1980, pp. 672 - 688
Copyright
Copyright © Applied Probability Trust 1980 

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References

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