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December 2020 Homogeneous mappings of regularly varying vectors
Piotr Dyszewski, Thomas Mikosch
Ann. Appl. Probab. 30(6): 2999-3026 (December 2020). DOI: 10.1214/20-AAP1579

Abstract

It is well known that the product of two independent regularly varying random variables with the same tail index is again regularly varying with this index. In this paper, we provide sharp sufficient conditions for the regular variation property of product-type functions of regularly varying random vectors, generalizing and extending the univariate theory in various directions. The main result is then applied to characterize the regular variation property of products of i.i.d. regularly varying quadratic random matrices and of solutions to affine stochastic recurrence equations under nonstandard conditions.

Citation

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Piotr Dyszewski. Thomas Mikosch. "Homogeneous mappings of regularly varying vectors." Ann. Appl. Probab. 30 (6) 2999 - 3026, December 2020. https://doi.org/10.1214/20-AAP1579

Information

Received: 1 March 2019; Revised: 1 February 2020; Published: December 2020
First available in Project Euclid: 14 December 2020

Digital Object Identifier: 10.1214/20-AAP1579

Subjects:
Primary: 60E05
Secondary: 62G20

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 6 • December 2020
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