{
  "abstract": "We construct finite Gamma convolutions approximating the first hitting time of $1$ by a Bessel process of index $ν>-1$ started at the origin. The scale measure in the classical exponential representation of this law is obtained by squaring the positive half of a dilated modified Lommel polynomial orthogonality measure. Its Jacobi recurrence yields an $N$-factor Gamma convolution that uniquely matches the first $2N$ cumulants, the maximal number attainable in this class. From an exact Gaussian quadrature remainder we derive supergeometric convergence of the Laplace transforms on compact subsets of a common slit plane and geometric convergence of the distribution functions uniformly on the real line. The approximants have total Gamma shape $N(N+ν+1)$, and their Laplace transforms and negative moments decrease to those of the exit law.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19233",
  "author_total": 1,
  "authors": [
    {
      "name": "Steven P. Clark"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bfxq1r64g48tv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19233",
  "fulltext_url": null,
  "id": "bfxq1r64g48tv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19233",
  "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",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7222005018",
  "pdf_url": "https://arxiv.org/pdf/2610.19233",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bfxq1r64g48tv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19233",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19233"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Moment-optimal Gamma approximation of Bessel Process exit times",
  "title_text": "Moment-optimal Gamma approximation of Bessel Process exit times",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/bfxq1r64g48tv",
  "venue": "arXiv",
  "versions": []
}