Shot-noise excursions and non-stabilizing Poisson functionals

Abstract : This article presents an asymptotic study of shot noise processes excursions, and of a more general class of statistics on marked spatial Poisson processes. A particularity of shot noise excursions, with respect to many popular objects of stochastic geometry, is that they are not stabilizing in general, but still a modification of the point process far from 0 will not modify the excursion set close to the origin by much. We shall present a complete second order theory that is applicable to stabilizing functionals, as well as non-stabilizing ones that satisfy this principle. This goes through a general mixing-type condition that adapts nicely to both proving asymptotic normality and volumic variance.
Type de document :
Pré-publication, Document de travail
MAP5 2017-30. 2017
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https://hal.archives-ouvertes.fr/hal-01654056
Contributeur : Raphael Lachieze-Rey <>
Soumis le : samedi 2 décembre 2017 - 19:00:45
Dernière modification le : mercredi 6 décembre 2017 - 01:13:06

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  • HAL Id : hal-01654056, version 1
  • ARXIV : 1712.01558

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Raphael Lachieze-Rey. Shot-noise excursions and non-stabilizing Poisson functionals. MAP5 2017-30. 2017. 〈hal-01654056〉

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