A criterion and a Cram\'er-Wold device for quasi-infinite divisibility for discrete multivariate probability laws
Abstract
Multivariate discrete probability laws are considered. We show that such laws are quasi-infinitely divisible if and only if their characteristic functions are separated from zero. We generalize the existing results for the univariate discrete laws and for the multivariate laws on Zd. The Cram\'er-Wold devices for infinite and quasi-infinite divisibility were proved.
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