Author:
Crane Harry,Mccullagh Peter
Abstract
Superposition is a mapping on point configurations that sends the n-tuple into the n-point configuration , counted with multiplicity. It is an additive set operation such that the superposition of a k-point configuration in is a kn-point configuration in . A Poisson superposition process is the superposition in of a Poisson process in the space of finite-length -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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference22 articles.
1. Alpha-permanents and their applications to mulivariate gamma, negative binomial and ordinary binomial distributions;Vere-Jones;New Zealand J. Math.,1997
2. A generalization of permanents and determinants
3. The permanental process
4. The coincidence approach to stochastic point processes
5. Determinantal Processes and Independence