MULTIVARIATE REGULAR VARIATION ON CONES: APPLICATION TO EXTREME VALUES, hIDDEN REGULAR VARIATION AND CONDITIONED LIMIT LAWS

Sidney Resnick

We attempt to bring some modest unity to three subareas of heavy tail analysis and extreme value theory: (i) limit laws for componentwise maxima of iid random variables; (ii) hidden regular variation and asymptotic independence; and (iii) 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: (a) the compactified first quadrant minus the origin; (b) the compactified first quadrant minus the axes through the origin; and (c) the compactified first quadrant minus one axis through the origin.