Work

Functionals of spatial point processes having a density with respect to the Poisson process

Year: 2014

Type: preprint

Abstract: U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito chaos expansion. In the second half we obtain more explicit results for a system of U-statistics of some parametric models in stochastic geometry. In the logaritmic form functionals are connected to Gibbs models. There is an inequality between moments of Poisson and non-Poisson functionals in this case, and we have a version of the central limit theorem in the Poisson case.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1401.2783

Authors: Benes, Viktor, Zikmundova, Marketa

Institutions: Charles University, University of Chemistry and Technology, Prague

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Grantová Agentura České Republiky

Award: Stochastic geometry - inhomogeneity, marking, dynamics and stereology

OpenAlex ID: W1966565271

Cites: 8

Cited by: 1

Related to: 20