Journal of Applied Probability

General inverse problems for regular variation

Ewa Damek, Thomas Mikosch, Jan Rosiński, and Gennady Samorodnitsky


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.

Article information

J. Appl. Probab., Volume 51A (2014), 229-248.

First available in Project Euclid: 2 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E05: Distributions: general theory
Secondary: 60F05: Central limit and other weak theorems

Regular variation inverse problem linear process Breiman's result random matrix


Damek, Ewa; Mikosch, Thomas; Rosiński, Jan; Samorodnitsky, Gennady. General inverse problems for regular variation. J. Appl. Probab. 51A (2014), 229--248. doi:10.1239/jap/1417528478.

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