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On the structure of regular infinitely divisible point processes

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  • Ammann, Larry P.
  • Thall, Peter F.

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.

Suggested Citation

  • Ammann, Larry P. & Thall, Peter F., 1977. "On the structure of regular infinitely divisible point processes," Stochastic Processes and their Applications, Elsevier, vol. 6(1), pages 87-94, November.
    • Handle: RePEc:eee:spapps:v:6:y:1977:i:1:p:87-94
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    Cited by:

    1. R. Milne & M. Westcott, 1993. "Generalized multivariate Hermite distributions and related point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 367-381, June.

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