## The Annals of Probability

- Ann. Probab.
- Volume 16, Number 2 (1988), 642-657.

### Inequalities for Multivariate Infinitely Divisible Processes

Lawrence D. Brown and Yosef Rinott

#### 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.

#### Article information

**Source**

Ann. Probab., Volume 16, Number 2 (1988), 642-657.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176991777

**Digital Object Identifier**

doi:10.1214/aop/1176991777

**Mathematical Reviews number (MathSciNet)**

MR929067

**Zentralblatt MATH identifier**

0646.60018

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60E05: Distributions: general theory

Secondary: 60G99: None of the above, but in this section 60K25: Queueing theory [See also 68M20, 90B22] 62G30: Order statistics; empirical distribution functions 62E99: None of the above, but in this section

**Keywords**

Slepian's inequality infinitely divisible distributions multivariate Poisson distribution queueing theory multivariate sample cumulative distribution functions

#### Citation

Brown, Lawrence D.; Rinott, Yosef. Inequalities for Multivariate Infinitely Divisible Processes. Ann. Probab. 16 (1988), no. 2, 642--657. doi:10.1214/aop/1176991777. https://projecteuclid.org/euclid.aop/1176991777