Non-localised Poisson functionals and shot noise excursions

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. 2018
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Contributeur : Raphael Lachieze-Rey <>
Soumis le : samedi 30 juin 2018 - 13:09:32
Dernière modification le : mardi 3 juillet 2018 - 07:06:37


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  • HAL Id : hal-01654056, version 2
  • ARXIV : 1712.01558



Raphael Lachieze-Rey. Non-localised Poisson functionals and shot noise excursions. MAP5 2017-30. 2018. 〈hal-01654056v2〉



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