Regularly varying measures on metric spaces: hidden regular variation and hidden jumps
type: Item
instance of: scholarly article
title: Regularly varying measures on metric spaces: hidden regular variation and hidden jumps
zbMATH Open document ID: 1317.60007
DOI: 10.1214/14-PS231
author: Filip Lindskog
author: Sidney I. Resnick
author: Joyjit Roy
published in: Probability Surveys
publication date: 2014-10-22T00:00:00Z
full work available at URL: https://arxiv.org/abs/1307.5803
full work available at URL: https://projecteuclid.org/euclid.ps/1413896892
reviewed by: Sophia L. Kalpazidou
Mathematics Subject Classification ID: 60B05
Mathematics Subject Classification ID: 28A33
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G70
zbMATH DE Number: 6359730
zbMATH Keywords: regular variation
zbMATH Keywords: multivariate heavy tails
zbMATH Keywords: tail estimation
zbMATH Keywords: hidden regular variation
zbMATH Keywords: \(M\)-convergence
zbMATH Keywords: Lévy process
MaRDI profile type: Publication
arXiv ID: 1307.5803
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review text: The authors study a general framework for regular variation and the so-called heavy tails for distributions on metric-space-valued random variables, with further applications to regular variation for measures on \(\mathbb{R}_+= [0,+\infty)\) and on the space of all real-valued, right-continuous functions having left limits on \([0,1]\).NEWLINENEWLINENEWLINEThe heavy tails occur in a variety of domains such as risk management, quantitative finance and economics, complex networks of data and telecommunication transmissions, and social networks. In the particular case of one dimension, the heavy tails are known as Pareto tails. The general mathematical framework for developing the heavy tails is the theory of regular variation, originally formulated on \([0,+\infty)\) and extended to more general spaces; see [\textit{N. H. Bingham} et al., Regular variation. Cambridge University Press (1987; Zbl 0617.26001); Paperback ed. (1989; Zbl 0667.26003)].NEWLINENEWLINE Finally, the authors attempt to clarify the proper definition of regular variation in metric spaces.
description: scientific article; zbMATH DE number 6359730