Translator Disclaimer
December 2015 Poisson superposition processes
Harry Crane, Peter McCullagh
Author Affiliations +
J. Appl. Probab. 52(4): 1013-1027 (December 2015). DOI: 10.1239/jap/1450802750

Abstract

Superposition is a mapping on point configurations that sends then-tuple(x1, . . ., xn) ∈ Xninto the n-point configuration{x1, . . ., xn} ⊂ X,counted with multiplicity. It is an additive set operation such that thesuperposition of a k-point configuration in Xnis a kn-point configuration in X. A Poisson superposition processis the superposition in X of a Poisson process in the space offinite-length X-valued sequences. From properties of Poisson processesas well as some algebraic properties of formal power series, we obtain anexplicit expression for the Janossy measure of Poisson superposition processes,and we study their law under domain restriction. Examples of well-known Poissonsuperposition processes include compound Poisson, negative binomial, andpermanental (boson) processes.

Citation

Download Citation

Harry Crane. Peter McCullagh. "Poisson superposition processes." J. Appl. Probab. 52 (4) 1013 - 1027, December 2015. https://doi.org/10.1239/jap/1450802750

Information

Published: December 2015
First available in Project Euclid: 22 December 2015

zbMATH: 1334.60080
MathSciNet: MR3439169
Digital Object Identifier: 10.1239/jap/1450802750

Subjects:
Primary: 60G55

Rights: Copyright © 2015 Applied Probability Trust

JOURNAL ARTICLE
15 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.52 • No. 4 • December 2015
Back to Top