Open Access
2014 Regularly varying measures on metric spaces: Hidden regular variation and hidden jumps
Filip Lindskog, Sidney I. Resnick, Joyjit Roy
Probab. Surveys 11: 270-314 (2014). DOI: 10.1214/14-PS231


We develop a framework for regularly varying measures on complete separable metric spaces $\mathbb{S}$ with a closed cone $\mathbb{C}$ removed, extending material in [15,24]. Our framework provides a flexible way to consider hidden regular variation and allows simultaneous regular-variation properties to exist at different scales and provides potential for more accurate estimation of probabilities of risk regions. We apply our framework to iid random variables in $\mathbb{R}_{+}^{\infty}$ with marginal distributions having regularly varying tails and to càdlàg Lévy processes whose Lévy measures have regularly varying tails. In both cases, an infinite number of regular-variation properties coexist distinguished by different scaling functions and state spaces.


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Filip Lindskog. Sidney I. Resnick. Joyjit Roy. "Regularly varying measures on metric spaces: Hidden regular variation and hidden jumps." Probab. Surveys 11 270 - 314, 2014.


Published: 2014
First available in Project Euclid: 21 October 2014

zbMATH: 1317.60007
MathSciNet: MR3271332
Digital Object Identifier: 10.1214/14-PS231

Primary: 28A33 , 60G17 , 60G51 , 60G70

Keywords: hidden regular variation , Lévy process , M-convergence , Multivariate heavy tails , regular variation , Tail estimation

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.11 • 2014
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