Publikace na Matematicko-fyzikální fakulta |
2014
Abstrakt
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-It^o 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.