arXiv subjects
Publications and source records attributed to I. A. Alexeev.
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 $\mathbb{Z}^d$. The Cramér-Wold devices for infinite and quasi-infinite divisibility were proved.
We consider discrete probability laws on the real line, whose characteristic functions are separated from zero. In particular, this class includes arbitrary discrete infinitely divisible laws and lattice probability laws, whose characteristic functions have no zeroes on the real line. We show that characteristic functions of such laws admit spectral Lévy--Khinchine type representations. We also apply the representations of such laws to obtain limit and compactness theorems with convergence in variation to probability laws from this class. Thus we generalize the corresponding results from the recent papers by Lindner, Pan, Sato, and by Khartov.