Integer valued stable random variables. (English) Zbl 1283.60022

Summary: The aim of this paper is to define the notion of stability for random variables on \(\mathbb{Z}\). A definition of discrete stable distributions is introduced and we study properties of such distributions. The generating functions are given, as well as the probabilities of lattice distribution. We show how these distributions converge to classical stable distributions and thus can be considered as a discrete approximation of their absolutely continuous counterparts.


60E07 Infinitely divisible distributions; stable distributions
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