English

Multivariate Regular Variation on Cones: Application to Extreme Values, Hidden Regular Variation and Conditioned Limit Laws

Probability 2009-09-29 v1

Abstract

We attempt to bring some modest unity to three subareas of heavy tail analysis and extreme value theory: limit laws for componentwise maxima of iid random variables;hidden regular variation and asymptotic independence;conditioned limit laws when one component of a random vector is extreme. The common theme is multivariate regular variation on a cone and the three cases cited come from specifying the cones [0,]d{0};(0,]d;[0,\infty]^d\setminus \{\boldsymbol 0\};(0,\infty]^d; and [0,]×(0,][0,\infty]\times (0,\infty].

Keywords

Cite

@article{arxiv.0712.3442,
  title  = {Multivariate Regular Variation on Cones: Application to Extreme Values, Hidden Regular Variation and Conditioned Limit Laws},
  author = {Sidney I. Resnick},
  journal= {arXiv preprint arXiv:0712.3442},
  year   = {2009}
}

Comments

To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.informaworld.com/openurl?genre=journal%26issn=1744-2508) edited by N.H. Bingham and I.V. Evstigneev which will be reprinted as Volume 57 of the IMS Lecture Notes Monograph Series (http://imstat.org/publications/lecnotes.htm)

R2 v1 2026-06-21T09:56:16.512Z