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Sampling cluster point processes: a review (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)
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The theme of this talk is the sampling of cluster and iterated cluster point processes. It is partially a review, mainly of the Brix–Kendall exact sampling method for cluster point processes and its adaptation by Moller and Rasmussen to Hawkes branching point processes on the real line with light-tail fertility rate. A formal proof via Laplace transforms of the validity of the method in terms of general clusters that are not necessarily point processes fits this purpose and allows to include the exact sampling of Boolean models. The main novel aspect of this review is the extension of the above sampling methods to non-Poissonian germ point processes.
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