Bounds for the probability generating functional of a Gibbs point process

Kaspar Stucki; Dominic Schuhmacher

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arXiv · 1210.4177

Bounds for the probability generating functional of a Gibbs point process

Kaspar Stucki·Dominic Schuhmacher

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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.

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BibTeX RIS

Kaspar Stucki, Dominic Schuhmacher. 2012-10-15. Bounds for the probability generating functional of a Gibbs point process. https://arxiv.org/abs/1210.4177

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