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.
Publié le : 2002-08-14
Classification:
Point process,
vague convergence,
multivariate regular variation,
heavy tailed distribution,
stochastic recurrence equation,
GARCH process,
60E05,
60G10,
60G55,
60G70,
62M10,
62P05
@article{1031863174,
author = {Basrak, Bojan and Davis, Richard A. and Mikosch, Thomas},
title = {A characterization of multivariate regular variation},
journal = {Ann. Appl. Probab.},
volume = {12},
number = {1},
year = {2002},
pages = { 908-920},
language = {en},
url = {http://dml.mathdoc.fr/item/1031863174}
}
Basrak, Bojan; Davis, Richard A.; Mikosch, Thomas. A characterization of multivariate regular variation. Ann. Appl. Probab., Tome 12 (2002) no. 1, pp. 908-920. http://gdmltest.u-ga.fr/item/1031863174/