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General inverse problems for regular variation

Part of: Distribution theory - Probability Limit theorems

Published online by Cambridge University Press:  30 March 2016

Ewa Damek ,
Thomas Mikosch ,
Jan Rosiński  and
Gennady Samorodnitsky
Ewa Damek
Affiliation:
University of Wrocław, Mathematical Institute, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland. Email address: ewa.damek@math.uni.worc.pl.
Thomas Mikosch
Affiliation:
Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark. Email address: mikosch@math.ku.dk.
Jan Rosiński
Affiliation:
Department of Mathematics, 227 Ayres Hall, University of Tennessee, Knoxville, TN 37996-1320, USA. Email address: rosinski@math.utk.edu.
Gennady Samorodnitsky
Affiliation:
School of Operations Research and Information Engineering, and Department of Statistics, Cornell University, 220 Rhodes Hall, Ithaca, NY 14853, USA. Email address: gs18@cornell.edu.
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Abstract

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Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed random object is caused by regular variation of components of the original random structure. In this paper we build on previous work, and derive results in the multivariate case and in situations where regular variation is not restricted to one particular direction or quadrant.

Keywords

Regular variationinverse problemlinear processBreiman's resultrandom matrix

MSC classification

Primary: 60E05: Distributions
Secondary: 60F05: Central limit and other weak theorems
Type
Part 6. Heavy tails
Information
Journal of Applied Probability , Volume 51 , Issue A: Celebrating 50 Years of The Applied Probability Trust , December 2014 , pp. 229 - 248
Copyright
Copyright © Applied Probability Trust 2014 

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