1. Functionals of spatial point processes having a density with respect to the Poisson process
- Creator:
- Beneš, Viktor and Zikmundová, Markéta
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- difference of a functional, limit theorem, moments, and U-statistics
- Language:
- English
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public