The Annals of Probability

Inequalities for Multivariate Infinitely Divisible Processes

Lawrence D. Brown and Yosef Rinott

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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


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