Stochastic Monotonicity and Slepian-Type Inequalities for Infinitely Divisible and Stable Random Vectors

Abstract

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