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February 2006 On Kesten's counterexample to the Cramér-Wold device for regular variation
Henrik Hult, Filip Lindskog
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Bernoulli 12(1): 133-142 (February 2006).


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 The construction is based on unpublished notes by Harry Kesten.


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Henrik Hult. Filip Lindskog. "On Kesten's counterexample to the Cramér-Wold device for regular variation." Bernoulli 12 (1) 133 - 142, February 2006.


Published: February 2006
First available in Project Euclid: 28 February 2006

zbMATH: 1108.60015
MathSciNet: MR2202325

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability


Vol.12 • No. 1 • February 2006
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