Open Access
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


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.


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

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

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

Keywords: GARCH process , heavy tailed distribution , multivariate regular variation , point process , stochastic recurrence equation , vague convergence

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.12 • No. 3 • August 2002
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