Non-localised Poisson functionals and shot noise excursions
Résumé
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.
Mots clés
Berry-Esseen bounds
random
excursions
stabilisation
MSC 2010 subject classifications: Primary 60D05
central limit theorem
and phrases: Poisson functionals
random excursions
Central limit theorems
central limit theorem
Shot noise fields
Shot noise fields
stabilisation
Berry-Esseen bounds
60G60
Poisson functionals
60F05
Domaines
Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
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