{
  "abstract": "Let $Z_α$ be a positive $α$-stable random variable, where $0<α<1$. We prove that $Z_α^p$ is infinitely divisible for every $p>0$. Combining this result with Jedidi and Simon's characterization of infinite divisibility of negative powers of $Z_α$, we obtain, for $p\\ne0$, $$Z_α^p\\ \\text{is infinitely divisible} \\quad\\Longleftrightarrow\\quad p\\in\\left(-\\infty,-\\fracα{1-α}\\right]\\cup(0,\\infty).$$ The proof relies on Kanter's factorization and a general product property: if $X$ is a mixture of exponential distributions, $W$ is a generalized gamma convolution, and $X$ and $W$ are independent, then $(X+c)W$ is infinitely divisible for every $c\\ge 0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31802",
  "author_total": 1,
  "authors": [
    {
      "name": "Min Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/amvbknj170ag2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31802",
  "fulltext_url": null,
  "id": "amvbknj170ag2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31802",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.31802",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/amvbknj170ag2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.31802",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31802"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Infinite divisibility of powers of positive stable random variables",
  "title_text": "Infinite divisibility of powers of positive stable random variables",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/amvbknj170ag2",
  "venue": "arXiv",
  "versions": []
}