Bounds for the probability generating functional of a Gibbs point process

Schuhmacher, Dominic; Stucki, Kaspar (2014). Bounds for the probability generating functional of a Gibbs point process. Advances in applied probability, 46(1), pp. 21-34. Applied Probability Trust 10.1239/aap/1396360101

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Schuhmacher, Dominic and Stucki, Kaspar

Subjects:

300 Social sciences, sociology & anthropology > 360 Social problems & social services
500 Science > 510 Mathematics
300 Social sciences, sociology & anthropology > 310 Statistics

ISSN:

0001-8678

Publisher:

Applied Probability Trust

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

15 Sep 2014 16:04

Last Modified:

19 Dec 2014 12:06

Publisher DOI:

10.1239/aap/1396360101

BORIS DOI:

10.7892/boris.51698

URI:

https://boris.unibe.ch/id/eprint/51698

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