## Journal of Applied Probability

### Poisson superposition processes

#### Abstract

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

#### Article information

Source
J. Appl. Probab., Volume 52, Number 4 (2015), 1013-1027.

Dates
First available in Project Euclid: 22 December 2015

https://projecteuclid.org/euclid.jap/1450802750

Digital Object Identifier
doi:10.1239/jap/1450802750

Mathematical Reviews number (MathSciNet)
MR3439169

Zentralblatt MATH identifier
1334.60080

Subjects
Primary: 60G55: Point processes

#### Citation

Crane, Harry; McCullagh, Peter. Poisson superposition processes. J. Appl. Probab. 52 (2015), no. 4, 1013--1027. doi:10.1239/jap/1450802750. https://projecteuclid.org/euclid.jap/1450802750

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