Filip Lindskog, KTH
 
The Cramér-Wold device for regular variation

Abstract:

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.  We discuss  counterexamples
showing that for integer-valued indices, regular variation of all
linear combinations does not imply that the vector is regularly
varying.  This has consequences, which are illustrated,  when one
tries to extend various univariate results on the tail behavior of
random variables to the multivariate setting.