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

Sidney I. Resnick

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arXiv · 0712.3442

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

Sidney I. Resnick

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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 $[0,\infty]^d\setminus \{\boldsymbol 0\};(0,\infty]^d;$ and $[0,\infty]\times (0,\infty]$.

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BibTeX RIS

Sidney I. Resnick. 2007-12-20. Multivariate Regular Variation on Cones: Application to Extreme Values, Hidden Regular Variation and Conditioned Limit Laws. https://arxiv.org/abs/0712.3442

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