Infinite divisibility of $α$-Cauchy distributions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908964604608512 |
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| author | Wang, Min |
| author_facet | Wang, Min |
| contents | In 2009, Yano, Yano and Yor proposed the question of studying the infinite divisibility of the $α$-Cauchy variable $\mathcal{C}_α$ for $α> 1$. The particular case $\mathcal{C}_2$ is the well-known standard Cauchy variable, which is infinitely divisible and indeed stable. For $α\neq 2$, the infinite divisibility of $\mathcal{C}_α$ is previously unknown. In this paper, we prove that $\mathcal{C}_α$ is infinitely divisible if and only if $1 < α\leq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23164 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite divisibility of $α$-Cauchy distributions Wang, Min Probability 60E07, 60E05, 60E10, 33E12 In 2009, Yano, Yano and Yor proposed the question of studying the infinite divisibility of the $α$-Cauchy variable $\mathcal{C}_α$ for $α> 1$. The particular case $\mathcal{C}_2$ is the well-known standard Cauchy variable, which is infinitely divisible and indeed stable. For $α\neq 2$, the infinite divisibility of $\mathcal{C}_α$ is previously unknown. In this paper, we prove that $\mathcal{C}_α$ is infinitely divisible if and only if $1 < α\leq 2$. |
| title | Infinite divisibility of $α$-Cauchy distributions |
| topic | Probability 60E07, 60E05, 60E10, 33E12 |
| url | https://arxiv.org/abs/2512.23164 |