Stochastic monotonicity and Slepian-type inequalities for infinitely divisible and stable random vectors

Gennady Samorodnitsky
Murad S. Taqqu

Abstract:

We study the relation between stochastic domination of an infinitely divisible random vector by another infinitely divisible random vector and their corresponding Lévy measures. The results are used to derive a Slepian-type inequality for a general class of symmetric infinitely divisible random vectors.