{
  "abstract": "Let X be a centered spectrally positive infinitely divisible random variable with finite nonzero variance V. We determine the smallest scale c in a right-sided sub-gamma bound whose quadratic proxy is fixed at V. A probability transform of the normalized Kolmogorov canonical measure produces a nonnegative variable R_X for which log E e^{tX} = V t^2 M_{R_X}(t)/2. The scale problem therefore reduces to comparing the MGF of R_X with that of an exponential law, leading to an exact one-dimensional variational formula. If X is non-Gaussian and has a positive exponential moment, the optimal scale is at least kappa_3(X)/(3V), with equality precisely when R_X belongs to the M-class of Klar and Mueller. Equality in the standard sub-gamma envelope occurs only for the Gaussian law or, in the non-Gaussian case, for centered compound Poisson laws with exponential jumps. For a general compound Poisson law, R_X is the second-order equilibrium distribution of the jump size. Exact calculations for gamma and bounded two-point jumps show that the optimum may occur at the origin, at the positive MGF boundary, or at an interior point.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00032",
  "author_total": 1,
  "authors": [
    {
      "name": "Yichuan Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/360zb6xhtavne.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00032",
  "fulltext_url": null,
  "id": "360zb6xhtavne",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00032",
  "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",
      "1803|Probability and Risk Models"
    ]
  ],
  "openalex": "W7216156739",
  "pdf_url": "https://arxiv.org/pdf/2610.00032",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/360zb6xhtavne.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00032",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00032"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Optimal Sub-Gamma Scales for Spectrally Positive Infinitely Divisible Laws",
  "title_text": "Optimal Sub-Gamma Scales for Spectrally Positive Infinitely Divisible Laws",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/360zb6xhtavne",
  "venue": "arXiv",
  "versions": []
}