Some criteria of rational-infinite divisibility for probability laws
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910601861660672 |
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| author | Khartov, A. A. |
| author_facet | Khartov, A. A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_14524 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some criteria of rational-infinite divisibility for probability laws Khartov, A. A. Probability 60E05, 60E07, 60E10 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. |
| title | Some criteria of rational-infinite divisibility for probability laws |
| topic | Probability 60E05, 60E07, 60E10 |
| url | https://arxiv.org/abs/2305.14524 |