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August 2002 A characterization of multivariate regular variation
Bojan Basrak, Richard A. Davis, Thomas Mikosch
Ann. Appl. Probab. 12(3): 908-920 (August 2002). DOI: 10.1214/aoap/1031863174

Abstract

We establish the equivalence between the multivariate regular variation of a random vector and the univariate regular variation of all linear combinations of the components of such a vector. According to a classical result of Kesten [Acta Math. 131 (1973) 207-248], this result implies that stationary solutions to multivariate linear stochastic recurrence equations are regularly varying. Since GARCH processes can be embedded in such recurrence equations their finite-dimensional distributions are regularly varying.

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Bojan Basrak. Richard A. Davis. Thomas Mikosch. "A characterization of multivariate regular variation." Ann. Appl. Probab. 12 (3) 908 - 920, August 2002. https://doi.org/10.1214/aoap/1031863174

Information

Published: August 2002
First available in Project Euclid: 12 September 2002

zbMATH: 1070.60011
MathSciNet: MR1925445
Digital Object Identifier: 10.1214/aoap/1031863174

Subjects:
Primary: 60E05
Secondary: 60G10, 60G55, 60G70, 62M10, 62P05

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.12 • No. 3 • August 2002
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