On Kesten's counterexample to the Cramér-Wold device for regular variation
Hult, Henrik ; Lindskog, Filip
Bernoulli, Tome 12 (2006) no. 2, p. 133-142 / Harvested from Project Euclid
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In 2002 Basrak, Davis and Mikosch showed that an analogue of the Cramér-Wold device holds for regular variation of random vectors if the index of regular variation is not an integer. This characterization is of importance when studying stationary solutions to stochastic recurrence equations. In this paper we construct counterexamples showing that for integer-valued indices, regular variation of all linear combinations does not imply that the vector is regularly varying. The construction is based on unpublished notes by Harry Kesten.
Publié le : 2006-02-14
Classification:  heavy-tailed distributions,  linear combinations,  multivariate regular variation 
@article{1141136653,
     author = {Hult, Henrik and Lindskog, Filip},
     title = {On Kesten's counterexample to the Cram\'er-Wold device for regular variation},
     journal = {Bernoulli},
     volume = {12},
     number = {2},
     year = {2006},
     pages = { 133-142},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1141136653}
}

Hult, Henrik; Lindskog, Filip. On Kesten's counterexample to the Cramér-Wold device for regular variation. Bernoulli, Tome 12 (2006) no. 2, pp.  133-142. http://gdmltest.u-ga.fr/item/1141136653/