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The Annals of Probability
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/∞ queues and of sample cumulative distribution functions for independent multivariate random variables.
Slepian's inequality, infinitely divisible distributions, multivariate Poisson distribution, queuing theory, multivariate sample cumulative distribution functions
Brown, L. D., & Rinott, Y. (1988). Inequalities for Multivariate Infinitely Divisible Processes. The Annals of Probability, 16 (2), 642-657. http://dx.doi.org/10.1214/aop/1176991777
Date Posted: 27 November 2017
This document has been peer reviewed.