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Pré-Publication, Document De Travail Année : 2018

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.
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Dates et versions

hal-01654056 , version 1 (02-12-2017)
hal-01654056 , version 2 (30-06-2018)
hal-01654056 , version 3 (13-12-2018)

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Raphaël Lachieze-Rey. Non-localised Poisson functionals and shot noise excursions. 2018. ⟨hal-01654056v2⟩
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