English

Bounds for the probability generating functional of a Gibbs point process

Probability 2013-04-18 v2 Statistics Theory Statistics Theory

Abstract

We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics like the F function. For pairwise interaction processes we obtain further estimates for the G and K functions, the intensity and higher order correlation functions. The proof of the main result is based on Stein's method for Poisson point process approximation.

Keywords

Cite

@article{arxiv.1210.4177,
  title  = {Bounds for the probability generating functional of a Gibbs point process},
  author = {Kaspar Stucki and Dominic Schuhmacher},
  journal= {arXiv preprint arXiv:1210.4177},
  year   = {2013}
}

Comments

15 pages

R2 v1 2026-06-21T22:22:10.415Z