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

2022/04/20 by Berger, David, Kutlu, Merve · 3 citations
#60E07 #60E10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2204.09651

Abstract

We consider distributions on 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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• Denseness in total variation and the class of rational-infinitely divisible distributions
• On necessary conditions of rational-infinite divisibility for distributions with non-zero discrete parts
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