2014/01/13 by Viktor Beneš, Benes, Viktor, Markéta Zikmundová +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #60D05 #60G55 #Diffusion and Search Dynamics #FOS: Mathematics #Morphological variations and asymmetry #Point processes and geometric inequalities #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1401.2783
openalex publication_date 2014/01/13 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
U-statistics of spatial point processes given by a density with respect to a\nPoisson process are investigated. In the first half of the paper general\nrelations are derived for the moments of the functionals using kernels from the\nWiener-Ito chaos expansion. In the second half we obtain more explicit results\nfor a system of U-statistics of some parametric models in stochastic geometry.\nIn the logaritmic form functionals are connected to Gibbs models. There is an\ninequality between moments of Poisson and non-Poisson functionals in this case,\nand we have a version of the central limit theorem in the Poisson case.\n