{
  "abstract": "In 2009, Yano, Yano and Yor asked whether the $α$-Cauchy distributions are self-decomposable or at least infinitely divisible in their study of hitting times for symmetric stable processes. Recently, the first named author proved that $α$-Cauchy distribution is infinitely divisible if and only if $1 < α\\leq 2$. In this paper, we prove that $α$-Cauchy distribution is self-decomposable if and only if $α= 2$. The proof is based on a new criterion for self-decomposability in the symmetric case. As an application, we show that the first hitting time of a nonzero point by a symmetric stable process of index $1<α<2$ starting from zero is not self-decomposable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18536",
  "author_total": 2,
  "authors": [
    {
      "name": "Min Wang"
    },
    {
      "name": "Sheng Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d8jzrs7hnxsk4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18536",
  "fulltext_url": null,
  "id": "d8jzrs7hnxsk4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18536",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7213508282",
  "pdf_url": "https://arxiv.org/pdf/2609.18536",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d8jzrs7hnxsk4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18536",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18536"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Self-decomposability of $α$-Cauchy distributions",
  "title_text": "Self-decomposability of α-Cauchy distributions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/d8jzrs7hnxsk4",
  "venue": "arXiv",
  "versions": []
}