| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2015-01-13T09:49:43Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144115 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| . |
