English

Sampling cluster point processes: a review

Probability 2016-04-25 v1

Abstract

The theme of this article 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 M{\o}ller and Rasmussen to Hawkes branching point processes on the real line with light-tail fertility rate are reviewed. The main novel aspect of this review is the extension to non-Poissonian germ point processes. For this, a slight adaptation is needed. 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.

Keywords

Cite

@article{arxiv.1604.06643,
  title  = {Sampling cluster point processes: a review},
  author = {Pierre Brémaud},
  journal= {arXiv preprint arXiv:1604.06643},
  year   = {2016}
}

Comments

17 pages

R2 v1 2026-06-22T13:38:34.981Z