Lévy measures of infinitely divisible random vectors and Slepian inequalities

Gennady Samorodnitsky
Murad S. Taqqu


We study Slepian inequalities for general non-Gaussian infinitely divisible random vectors. Conditions for such inequalities are expressed in terms of the corresponding Lévy measures of these vectors. These conditions are shown to be nearly best possible, and for a large subfamily of these conditions are necessary and sufficient for Slepian inequalities. As an application we consider Ornstein-Uhlenbeck processes and a family of introduced by Brown and Rinott.