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arXiv · 2305.14524

Some criteria of rational-infinite divisibility for probability laws

A. A. Khartov
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Abstract

We study the class $\boldsymbol{Q}$ of distribution functions $F$ that have the property of rational-infinite divisibility: there exist some infinitely divisible distribution functions $F_1$ and $F_2$ such that $F_1=F*F_2$. The class $\boldsymbol{Q}$ is a wide natural extension of the fundamental class of infinitely divisible distribution functions. We are interested in general conditions to belong to the class $\boldsymbol{Q}$ in terms of characteristic functions. We obtain criteria that seem to be convenient for the application for some cases, and we illustrate it by several examples in the paper.

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A. A. Khartov. 2023-05-23. Some criteria of rational-infinite divisibility for probability laws. https://arxiv.org/abs/2305.14524

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