MPS-RR 2002-18
May 2002

Shot noise Cox processes

Jesper Møller

Abstract

Shot noise Cox processes constitute a large class of Cox and Poisson cluster processes in $\mathbb{R}^d$, including Neyman-Scott, Poisson-Gamma, and shot noise G Cox processes. It is demonstrated that due to the structure of such models, a number of useful and general results can easily be established. The focus is on the probabilistic aspects with a view to statistical applications, particularly results for summary statistics, reduced Palm distributions, simulation with or without edge effects, conditional simulation of the intensity function, and local and global Markov properties.

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