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Results in the asymptotic and equilibrium theory of Poisson cluster processes

Published online by Cambridge University Press:  14 July 2016

M. Westcott
M. Westcott*
Affiliation:
Imperial College, London
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Abstract

This paper contains a detailed study of the Poisson cluster process on the real line, concentrating on two aspects; first, the asymptotic distribution of the number of points in [0,t) as t→ ∞ for both transient and equilibrium cluster processes and, secondly, a general formula for the probability generating function of the equilibrium process. Asymptotic formulae for cumulants of the process are also derived. The results obtained generalize those of previous writers. The approach is analytical, in contrast to the probabilistic treatment of P. A. W. Lewis.

Keywords

POINT PROCESSPOISSON CLUSTER PROCESSEQUILIBRIUM CLUSTER PROCESSLIMIT THEOREMS FOR CLUSTER PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 807 - 823
Copyright
Copyright © Applied Probability Trust 1973 

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