"Functionals of spatial point processes having a density with respect to the Poisson process" . "Zikmundov\u00E1, Mark\u00E9ta" . "RIV/00216208:11320/14:10283277" . "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." . "U-statistic; moments; limit theorem; difference of a functional"@en . . "Functionals of spatial point processes having a density with respect to the Poisson process" . . "0023-5954" . "11320" . "CZ - \u010Cesk\u00E1 republika" . . "Functionals of spatial point processes having a density with respect to the Poisson process"@en . . . "RIV/00216208:11320/14:10283277!RIV15-MSM-11320___" . "18"^^ . . . "10.14736/kyb-2014-6-0896" . "Functionals of spatial point processes having a density with respect to the Poisson process"@en . "6" . . . . "2"^^ . "Bene\u0161, Viktor" . "1"^^ . "[1EE48C031C10]" . . . "17684" . . "50" . "I, P(GAP201/10/0472)" . . . . "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."@en . . "Kybernetika" .