Quasi-infinite divisibility of a class of distributions with discrete part

David Berger; Merve Kutlu

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arXiv · 2204.09651

Quasi-infinite divisibility of a class of distributions with discrete part

David Berger·Merve Kutlu

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Abstract

We consider distributions on $\mathbb{R}$ that can be written as the sum of a non-zero discrete distribution and an absolutely continuous distribution. We show that such a distribution is quasi-infinitely divisible if and only if its characteristic function is bounded away from zero, thus giving a new class of quasi-infinitely divisible distributions. Moreover, for this class of distributions we characterize the existence of the $g$-moment for certain functions $g$.

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David Berger, Merve Kutlu. 2022-04-20. Quasi-infinite divisibility of a class of distributions with discrete part. https://arxiv.org/abs/2204.09651

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