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Further results for Gauss-Poisson processes

Published online by Cambridge University Press:  01 July 2016

R. K. Milne  and
M. Westcott
R. K. Milne*
Affiliation:
The Australian National University
M. Westcott*
Affiliation:
The Australian National University
*
∗ Now at London School of Economics.
∗∗ Now at Imperial College, University of London.
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Abstract

Newman (1970) introduced an interesting new class of point processes which he called Gauss-Poisson. They are characterized, in the most general case, by two measures. We determine necessary and sufficient conditions on these measures for the resulting point process to be well defined, and proceed to a systematic study of its properties. These include stationarity, ergodicity, and infinite divisibility. We mention connections with other classes of point processes and some statistical results. Our basic approach is through the probability generating functional of the process.

Keywords

POINT PROCESSESGAUSS-POISSON PROCESSESPROBABILITY GENERATING FUNCTIONALINFINITELY DIVISIBLE POINT PROCESSBIVARIATE POINT PROCESSDOUBLY STOCHASTIC POINT PROCESSPOISSON CLUSTERING PROCESSMIXING POINT PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 4 , Issue 1 , April 1972 , pp. 151 - 176
Copyright
Copyright © Applied Probability Trust 1972 

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