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A note on the non-homogeneous poisson cluster process

Published online by Cambridge University Press:  14 July 2016

Mark Westcott
Mark Westcott*
Affiliation:
C. S. I. R. O. Division of Mathematics and Statistics, Canberra
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Abstract

It is proved that, in a non-homogeneous Poisson cluster process whose cluster centre rate is λ(t), the long-term behaviour of several associated quantities is equivalent to their behaviour in a homogeneous process with centre rate Λ and the same cluster structure if λ(t)→ λ as t→∞.

Keywords

ASYMPTOTIC STATIONARITYEQUILIBRIUM POINT PROCESSLIMIT THEOREMS FOR CLUSTER PROCESSESNON-HOMOGENEOUS POISSON CLUSTER PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 396 - 398
Copyright
Copyright © Applied Probability Trust 1977 

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References

[1] Lewis, P. A. W. (1967) Non-homogeneous branching Poisson processes. J. R. Statist. Soc. B 29, 343–354.Google Scholar
[2] Westcott, M. (1971) On existence and mixing results for cluster point processes. J. R. Statist. Soc. B 33, 290–300.Google Scholar
[3] Westcott, M. (1973) Some results in the asymptotic and equilibrium theory of Poisson cluster processes. J. Appl. Prob. 10, 807–823.CrossRefGoogle Scholar