Regular variation in the mean and stable limits for Poisson shot noise
type: Item
instance of: scholarly article
title: Regular variation in the mean and stable limits for Poisson shot noise
zbMATH Open document ID: 1044.60013
author: Claudia Klüppelberg
author: Anette Schärf
author: T. Mikosch
published in: Bernoulli
publication date: 2004-06-18T00:00:00Z
review text: The authors study the limiting behaviour of Poisson shot noise when the limits are infinite-variance stable processes. In this context a sufficient condition for this convergence turns up which is closely related to multivariate regular variation. The authors also show that the latter condition is necessary and sufficient for the weak convergence of the point processes constructed from the normalized noise sequence and also for the weak convergence of its extremes.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 2075978
zbMATH Keywords: Poisson random measure
zbMATH Keywords: infinitely divisible distribution
zbMATH Keywords: multivariate regular variation
zbMATH Keywords: self-similar process
zbMATH Keywords: stable process
zbMATH Keywords: weak convergence
reviewed by: Zdzisław Rychlik
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3150/bj/1065444814
OpenAlex ID: W2032370704
DOI: 10.3150/BJ/1065444814
description: scientific article; zbMATH DE number 2075978