Functionals of spatial point process having density with respect to the Poisson process
| Autor: | Markéta Zikmundová, Viktor Beneš |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Process (computing)
Poisson process Poisson distribution Point process Theoretical Computer Science symbols.namesake Artificial Intelligence Control and Systems Engineering symbols Applied mathematics Electrical and Electronic Engineering Stochastic geometry Software Information Systems Mathematics Central limit theorem |
| Zdroj: | Kybernetika. :896-913 |
| ISSN: | 1805-949X 0023-5954 |
| DOI: | 10.14736/kyb-2014-6-0896 |
| Popis: | U-statistics of spatial point processes given by a density with respect to a Pois- son 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-Ito chaos expansion. In the second half we obtain more explicit results for a special system of U-statistics from stochastic geometry. In the logaritmic form func- tionals 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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