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A characterization of the Poisson process

Published online by Cambridge University Press:  14 July 2016

Pushpa Lata Gupta  and
Ramesh C. Gupta
Pushpa Lata Gupta*
Affiliation:
University of Maine at Orono
Ramesh C. Gupta*
Affiliation:
University of Maine at Orono
*
∗Postal address: Department of Mathematics, University of Maine, Orono, ME 04469, USA.
∗Postal address: Department of Mathematics, University of Maine, Orono, ME 04469, USA.
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Abstract

Denoting by v(t) the residual life of a component in a renewal process, Çinlar and Jagers (1973) and Holmes (1974) have shown that if E(v(t)) is independent of t for all t, then the process is Poisson. In this note we prove, under mild conditions, that if E(G(v(t))) is constant, then the process is Poisson. In particular if E((v(t))r) for some specific real number r ≧ 1 is independent of t, then the process is Poisson.

Keywords

RESIDUAL LIFE MOMENT
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 1 , March 1986 , pp. 233 - 235
Copyright
Copyright © Applied Probability Trust 1986 

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References

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