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Generalised shot noise Cox processes

  • Jesper Møller (a1) and Giovanni Luca Torrisi (a2)

Abstract

We introduce a class of Cox cluster processes called generalised shot noise Cox processes (GSNCPs), which extends the definition of shot noise Cox processes (SNCPs) in two directions: the point process that 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, second, on how to simulate such processes. In particular, results on 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 in important special cases of GSNCPs, and we discuss their relation to the corresponding results for SNCPs.

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Copyright

Corresponding author

Postal address: Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg, Denmark. Email address: jm@math.auc.dk
Postal address: CNR-Istituto per le Applicazioni del Calcolo ‘M. Picone’, Viale del Policlinico 137, I-00161 Rome, Italy. Email address: torrisi@iac.rm.cnr.it

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Generalised shot noise Cox processes

  • Jesper Møller (a1) and Giovanni Luca Torrisi (a2)

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