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Two mean values which characterize the Poisson process

Published online by Cambridge University Press:  14 July 2016

Erhan Çinlar  and
Peter Jagers
Erhan Çinlar
Affiliation:
Northwestern and Stanford Universities
Peter Jagers
Affiliation:
University of Göteborg
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Abstract

The Poisson process enjoys two special properties: the mean forward recurrence time at time t does not depend on t, and the mean backward recurrence time at time t is the “mean” of the interval distribution truncated at t. Poisson process is the only renewal process with these properties.

Keywords

POISSON PROCESSCHARACTERIZATION THEOREMSRENEWAL PROCESSESFORWARD RECURRENCE TIMESBACKWARD RECURRENCE TIMES
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 3 , September 1973 , pp. 678 - 681
Copyright
Copyright © Applied Probability Trust 1973 

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Footnotes

Research done at Stanford University under the partial support of A.F.O.S.R. Contract F 44620-67-C-0049 and N.S.F. Grant GP 15909.

References

[1] Chung, K. L. (1972) The Poisson process as a renewal process. Periodica Mathematica Hungar. 2, 41–48.Google Scholar