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A note on multivariate Poisson flows on stochastic processes

Published online by Cambridge University Press:  01 July 2016

Frederick J. Beutler
Frederick J. Beutler*
Affiliation:
The University of Michigan
*
∗Postal address: Computer, Information and Control Engineering Program, The University of Michigan, Ann Arbor, MI 48109, U.S.A.
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Abstract

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In [1], a deterministic counting rate condition is shown to be necessary and sufficient for a counting process induced on a Markov step process Z to be multivariate Poisson. We show here that the result continues to hold without Z being a Markov step process.

Keywords

MARKOV STEP PROCESS
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 15 , Issue 1 , March 1983 , pp. 219 - 220
Copyright
Copyright © Applied Probability Trust 1983 

References

[1] Beutler, F. J. and Melamed, B. (1982) Multivariate Poisson flows on Markov step processes. J. Appl. Prob. 19, 289–300.Google Scholar
[2] Brémaud, P. (1981) Point Processes and Queues: Martingale Dynamics. Springer-Verlag, New York.Google Scholar