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Regularly varying measures on metric spaces : Hidden regular variation and hidden jumps
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- Lindskog, Filip (author)
- KTH,Matematik (Inst.)
- Resnick, S. I. (author)
- Roy, J. (author)
- KTH Matematik (Inst) (creator_code:org_t)
- Institute of Mathematical Statistics, 2014
- 2014
- English.
- In: Probability Surveys. - : Institute of Mathematical Statistics. - 1549-5787. ; 11:2014, s. 270-314
- Journal article (peer-reviewed)
Abstract
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- We develop a framework for regularly varying measures on complete separable metric spaces S with a closed cone 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 ℝ∞+ 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
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- ref (subject category)
- art (subject category)
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