The Annals of Probability

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

Gennady Samorodnitsky and Murad S. Taqqu

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 21, Number 1 (1993), 143-160.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989397

Digital Object Identifier
doi:10.1214/aop/1176989397

Mathematical Reviews number (MathSciNet)
MR1207219

Zentralblatt MATH identifier
0771.60017

JSTOR
links.jstor.org

Subjects
Primary: 60E07: Infinitely divisible distributions; stable distributions
Secondary: 60E15: Inequalities; stochastic orderings

Keywords
Stochastic domination Slepian inequality infinitely divisible distributions stable distributions

Citation

Samorodnitsky, Gennady; Taqqu, Murad S. Stochastic Monotonicity and Slepian-Type Inequalities for Infinitely Divisible and Stable Random Vectors. Ann. Probab. 21 (1993), no. 1, 143--160. doi:10.1214/aop/1176989397. https://projecteuclid.org/euclid.aop/1176989397


Export citation