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.
Lawrence D. Brown. Yosef Rinott. "Inequalities for Multivariate Infinitely Divisible Processes." Ann. Probab. 16 (2) 642 - 657, April, 1988. https://doi.org/10.1214/aop/1176991777