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A characterization of the Poisson process using forward recurrence times

Published online by Cambridge University Press:  24 October 2008

Valerie Isham ,
D. N. Shanbhag  and
M. Westcott
Valerie Isham
Affiliation:
Department of Mathematics, Imperial College, London
D. N. Shanbhag
Affiliation:
Department of Probability and Statistics, University of Sheffield
M. Westcott
Affiliation:
Department of Mathematics, Imperial College, London
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Extract

Consider a renewal process on the nonnegative real line with non-arithmetic distribution function F(x). Denote by V(x; t) the distribution function of the forward recurrence time from t, t ≤ 0. If t is chosen at random with distribution function Ф(t), the corresponding unconditional forward recurrence time has distribution function

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 3 , November 1975 , pp. 513 - 516
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

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