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  • 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-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)
Title
  • Functionals of spatial point processes having a density with respect to the Poisson process
  • Functionals of spatial point processes having a density with respect to the Poisson process (en)
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  • Functionals of spatial point processes having a density with respect to the Poisson process
  • Functionals of spatial point processes having a density with respect to the Poisson process (en)
skos:notation
  • RIV/00216208:11320/14:10283277!RIV15-MSM-11320___
http://linked.open...avai/riv/aktivita
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  • I, P(GAP201/10/0472)
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  • 6
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  • 17684
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  • RIV/00216208:11320/14:10283277
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  • U-statistic; moments; limit theorem; difference of a functional (en)
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  • CZ - Česká republika
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  • [1EE48C031C10]
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  • Kybernetika
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  • 50
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  • Beneš, Viktor
  • Zikmundová, Markéta
issn
  • 0023-5954
number of pages
http://bibframe.org/vocab/doi
  • 10.14736/kyb-2014-6-0896
http://localhost/t...ganizacniJednotka
  • 11320
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