On the structure of regular infinitely divisible point processes

Larry P. Ammann; Peter F. Thall

doi:10.1016/0304-4149(77)90020-5

On the structure of regular infinitely divisible point processes

Larry P. Ammann, Peter F. Thall

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

A representation for the probability generating functional (p.g.fl.) of a regular infinitely divisible (i.d.) stochastic point process, motivated as a generalization of the Gauss-Poisson process, is presented. The functional is characterized by a sequence of Borel product measures. Necessary and sufficient conditions, in terms of these Borel measures, are given for this representation to be a p.g.fl., thus characterizing all regular i.d. point processes.

Original language	English (US)
Pages (from-to)	87-94
Number of pages	8
Journal	Stochastic Processes and their Applications
Volume	6
Issue number	1
DOIs	https://doi.org/10.1016/0304-4149(77)90020-5
State	Published - Nov 1977
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/0304-4149(77)90020-5

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AB - A representation for the probability generating functional (p.g.fl.) of a regular infinitely divisible (i.d.) stochastic point process, motivated as a generalization of the Gauss-Poisson process, is presented. The functional is characterized by a sequence of Borel product measures. Necessary and sufficient conditions, in terms of these Borel measures, are given for this representation to be a p.g.fl., thus characterizing all regular i.d. point processes.

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On the structure of regular infinitely divisible point processes

Abstract

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