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Regenerative multivariate point processes

Published online by Cambridge University Press:  01 July 2016

Mark Berman
Mark Berman*
Affiliation:
Imperial College, London
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Abstract

A class of stationary multivariate point processes is considered in which the events of one of the point processes act as regeneration points for the entire multivariate process. Some important properties of such processes are derived including the joint probability generating function for numbers of events in an interval of fixed length and the asymptotic behaviour of such processes. The general theory is then applied in three bivariate examples. Finally, some simple monotonicity results for stationary and renewal point processes (which are used in the second example) are proved in two appendices.

Keywords

POINT PROCESSMULTIVARIATE POINT PROCESSSTATIONARITYPOISSON PROCESSREGENERATIVE STOCHASTIC PROCESSRENEWAL PROCESSMARKOV RENEWAL PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 2 , June 1978 , pp. 411 - 430
Copyright
Copyright © Applied Probability Trust 1978 

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