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Selective interaction of a Poisson and renewal process: first-order stationary point results

Published online by Cambridge University Press:  14 July 2016

A. J. Lawrance
A. J. Lawrance*
Affiliation:
University of Leicester
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Abstract

The simple stationarity of a previously derived equilibrium process of responses in a renewal inhibited stationary point process is established by deriving the joint distribution of the number of responses in contiguous intervals in the process. For a renewal inhibited Poisson process the variancetime function of the process is obtained; the distribution of an arbitrary between-response interval and the synchronous counting distribution are also derived following analytic justification of the required results. These results strengthen earlier results in the theory of stationary point processes. Three other point processes arising from the interaction are briefly discussed.

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 359 - 372
Copyright
Copyright © Applied Probability Trust 1970 

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