Bounds for the probability generating functional of a Gibbs point process

2012/10/15 by Kaspar Stucki, Stucki, Kaspar, Dominic Schuhmacher +1
Mathematics · #60G55 #62M30 #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1210.4177

openalex publication_date 2012/10/15 · openalex created_date 2022/10/06 · openalex updated_date 2026/08/01

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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