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The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics

Funded by The Danish National Research Foundation

MPS-RR 2004-10
March 2004

Generalised Shot Noise Cox Processes

by: Giovanni Luca Torrisi , Jesper Møller


We introduce a new class of Cox cluster processes called generalised shotnoise Cox processes (GSNCPs), which extends the definition of shot noise Cox processes (SNCPs) in two directions: the point process which drives the shot noise is not necessarily Poisson, and the kernel of the shot noise can be random. Thereby a very large class of models for aggregated or clustered point patterns is obtained. Due to the structure of GSNCPs, a number of useful results can be established. We focus first on deriving summary statistics for GSNCPs and next on how to make simulation for GSNCPs. Particularly, results for first and second order moment measures, reduced Palm distributions, the $J$-function, simulation with or without edge effects, and conditional simulation of the intensity function driving a GSNCP are given. Our results are exemplified for special important cases of GSNCPs, and we discuss the relation to corresponding results for SNCPs.

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This paper has now been published in Adv. Appl. Prob. (to appear)