On multivariate infinitely divisible distributions

Roger A. Horn and F. W. Steutel

Stochastic Processes and their Applications, 1978, vol. 6, issue 2, 139-151

Abstract: Simple conditions are given which characterize the generating function of a nonnegative multivariate infinitely divisible random vector. Necessary conditions on marginals, linear combinations, tail behavior, and zeroes are discussed, and a sufficient condition is given. The latter condition, which is a multivariate generalization of ordinary log-convexity, is shown to characterize only certain products of univariate infinitely divisible distributions.

Date: 1978
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