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Properties of the bivariate delayed Poisson process

Published online by Cambridge University Press:  14 July 2016

A. J. Lawrance  and
P. A. W. Lewis
A. J. Lawrance
Affiliation:
University of Birmingham
P. A. W. Lewis
Affiliation:
Naval Postgraduate School, Monterey, California
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Abstract

The bivariate Poisson point process introduced in Cox and Lewis (1972), and there called the bivariate delayed Poisson process, is studied further; the process arises from pairs of delays on the events of a Poisson process. In particular, results are obtained for the stationary initial conditions, the joint distribution of the number of operative delays at an arbitrary time, the asynchronous counting distribution, and two semi-synchronous interval distributions. The joint delay distribution employed allows for dependence and two-sided delays, but the model retains the independence between different pairs of delays.

Keywords

BIVARIATE POISSON POINT PROCESSRANDOM DELAYS OF POISSON EVENTSINFINITE DIVISIBILITYASYNCHRONOUS COUNTINGSEMI-SYNCHRONOUS INTERVALS
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 257 - 268
Copyright
Copyright © Applied Probability Trust 1975 

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References

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