### Inequalities for Multivariate Infinitely Divisible Processes

Lawrence D. Brown and Yosef Rinott
Source: Ann. Probab. Volume 16, Number 2 (1988), 642-657.

#### Abstract

We describe a general class of multivariate infinitely divisible distributions and their related stochastic processes. Then we prove inequalities which are the analogs of Slepian's inequality for these distributions. These inequalities are applied to the distributions of $M/G/\infty$ queues and of sample cumulative distribution functions for independent multivariate random variables.

First Page:
Primary Subjects: 60E05
Secondary Subjects: 60G99, 60K25, 62G30, 62E99
Full-text: Open access