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

Title:

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

Creator:

Beneš, Viktor and Zikmundová, Markéta

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a8ee49b3-a209-43ac-b8f1-e6255b31eb3f
uuid:a8ee49b3-a209-43ac-b8f1-e6255b31eb3f

Subject:

difference of a functional, limit theorem, moments, and U-statistics

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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-Itô 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 logarithmic 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[896]-913

Source:

Kybernetika | 2014 Volume:50 | Number:6

Harvested from:

CDK

Metadata only:

false