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

نویسندگان

  • Viktor Benes
  • Markéta Zikmundová
چکیده

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.

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عنوان ژورنال:
  • Kybernetika

دوره 50  شماره 

صفحات  -

تاریخ انتشار 2014