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Thinning of point processes—covariance analyses

Published online by Cambridge University Press:  01 July 2016

Jagadeesh Chandramohan ,
Robert D. Foley  and
Ralph L. Disney
Jagadeesh Chandramohan*
Affiliation:
Case Western Reserve University
Robert D. Foley*
Affiliation:
Virginia Polytechnic Institute and State University
Ralph L. Disney*
Affiliation:
Virginia Polytechnic Institute and State University
*
∗Postal address: Department of Operations Research, Case Western Reserve University, Cleveland, OH 44106, USA.
∗∗ Postal address: Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
∗∗ Postal address: Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
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Abstract

Cross-covariances between the Bernoulli thinned processes of an arbitrary point process are determined. When the point process is renewal it is shown that zero correlation implies independence. An example is given to show that zero covariance between intervals does not imply zero covariance between counts. Mark-dependent thinning of Markov renewal processes is discussed and the results are applied to the overflow queue. Here we give an example of two uncorrelated but dependent renewal processes, neither of which is Poisson, which yield a Poisson process when superposed. Finally, we study Markov-chain thinning of renewal processes.

Keywords

MARK-DEPENDENT THINNINGMARKOV RENEWAL PROCESSESCROSS-CORRELATIONSRENEWAL PROCESSESSUPERPOSITION
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 1 , March 1985 , pp. 127 - 146
Copyright
Copyright © Applied Probability Trust 1985 

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References

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