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

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

2007-12-20

arxiv.org/abs/0712.3442v1

Mathematics

Probability

To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.i

Scientific paper

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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