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A characterization of the Poisson process

Published online by Cambridge University Press:  14 July 2016

S. M. Samuels
S. M. Samuels*
Affiliation:
Purdue University
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Abstract

Theorem: A necessary and sufficient condition for the superposition of two ordinary renewal processes to again be a renewal process is that they be Poisson processes.

A complete proof of this theorem is given; also it is shown how the theorem follows from the corresponding one for the superposition of two stationary renewal processes.

Keywords

POISSON PROCESSRENEWAL PROCESSSUPERPOSITIONSTATIONARY PROCESSPALM PROBABILITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 72 - 85
Copyright
Copyright © Applied Probability Trust 1974 

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References

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