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Title: Functionals of spatial point processes having a density with respect to the Poisson process (English)
Author: Beneš, Viktor
Author: Zikmundová, Markéta
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 50
Issue: 6
Year: 2014
Pages: 896-913
Summary lang: English
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Category: math
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Summary: $U$-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. (English)
Keyword: difference of a functional
Keyword: limit theorem
Keyword: moments
Keyword: U-statistics
MSC: 60D05
MSC: 60F05
MSC: 60G55
idZBL: Zbl 06416866
idMR: MR3301778
DOI: 10.14736/kyb-2014-6-0896
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Date available: 2015-01-13T09:49:43Z
Last updated: 2016-01-03
Stable URL: http://hdl.handle.net/10338.dmlcz/144115
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