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Two dependent Poisson processes whose sum is still a Poisson process

Published online by Cambridge University Press:  14 July 2016

Jean Jacod
Jean Jacod*
Affiliation:
Princeton University
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Abstract

We show that there exists a pair of Poisson processes which are not stochastically independent, and whose sum is still a Poisson process.

Keywords

POISSON PROCESSDEPENDENCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 170 - 172
Copyright
Copyright © Applied Probability Trust 1975 

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Footnotes

Research conducted while the author held a US-France exchange award from the National Science Foundation.

References

Cox, D. R. and Lewis, P. A. W. (1972) Multivariate point processes. Proc . Sixth Berkeley Symp. 3, 401–448.Google Scholar
Moran, P. A. P. (1967) A non-Markovian quasi-Poisson process. Studia Sci. Math. Hungar. 2, 425–429.Google Scholar
Serfling, R. J. (1973) Construction of dependent uncorrelated random variables with prescribed marginal distributions. Report M 268, Florida State University.Google Scholar