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March 2014 Bounds for the probability generating functional of a Gibbs point process
Kaspar Stucki, Dominic Schuhmacher
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Adv. in Appl. Probab. 46(1): 21-34 (March 2014). DOI: 10.1239/aap/1396360101

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 such as 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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Kaspar Stucki. Dominic Schuhmacher. "Bounds for the probability generating functional of a Gibbs point process." Adv. in Appl. Probab. 46 (1) 21 - 34, March 2014. https://doi.org/10.1239/aap/1396360101

Information

Published: March 2014
First available in Project Euclid: 1 April 2014

zbMATH: 1295.60061
MathSciNet: MR3189046
Digital Object Identifier: 10.1239/aap/1396360101

Subjects:
Primary: 60G55
Secondary: 62M30

Rights: Copyright © 2014 Applied Probability Trust

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Vol.46 • No. 1 • March 2014
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