Pareto Lévy measures and multivariate regular variation
type: Item
instance of: scholarly article
zbMATH Open document ID: 1248.60052
author: Irmingard Eder
author: Claudia Klüppelberg
published in: Advances in Applied Probability
publication date: 2012-04-10T00:00:00Z
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60G52
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 62H05
zbMATH DE Number: 6022666
zbMATH Keywords: multivariate Lévy processes
zbMATH Keywords: Pareto--Lévy copula
zbMATH Keywords: Lévy measure
zbMATH Keywords: multivariate regular variation
zbMATH Keywords: multivariate stable processes
zbMATH Keywords: spectral measure
zbMATH Keywords: tail integral
zbMATH Keywords: tail dependence coefficient
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1239/aap/1331216647
OpenAlex ID: W2094451824
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DOI: 10.1239/AAP/1331216647
title: Pareto Lévy measures and multivariate regular variation
review text: The authors consider regular variation of an \(\mathbb R^d\)-valued Lévy process \(X\) with Lévy measure \(\Pi\), emphasizing the dependence between jumps of its components. By transforming the marginal Lévy measures to those of a standard \(1\)-stable Lévy process, they decouple the marginal Lévy measure from the dependence structure. The dependence between the jumps is modeled by the so-called Pareto Lévy measure. The authors characterize the multivariate regular variation of \(X\) by its one-dimensional marginal Lévy measures and the Pareto Lévy measure.
reviewed by: Zakhar Kabluchko
description: scientific article; zbMATH DE number 6022666