{
  "abstract": "This paper is devoted to unifying the uniform local large-deviation asymptotics for a centered Lévy process $X$ with subexponential jumps. Our results assert that for any $θ,δ_0>0$ and $K\\geq0$, $$\\lim_{t\\to\\infty}\\sup_{x\\geqθt}\\sup_{|y|\\leq Kb(x)}\\sup_{δ\\in[δ_0,\\infty]}\\sup_{0<s\\leq t}\\bigg|\\frac{\\mathbf P\\big(X_s\\in(x-y,x-y+δ]\\big)}{s\\cdot\\mathbf P\\big(X_1\\in(x,x+δ]\\big)}-1\\bigg|=0,$$ where the natural-scale function $b$ satisfies a polynomial growth condition. This provides a continuous-time and simultaneously uniform analogue of the results of Denisov et al. [Ann. Probab., 2008], while being established under a weaker moment assumption.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.11637",
  "author_total": 2,
  "authors": [
    {
      "name": "Hao Wu"
    },
    {
      "name": "Wei Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1fx7z1bee5v90.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.11637",
  "fulltext_url": null,
  "id": "1fx7z1bee5v90",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.11637",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1803|Probability and Risk Models"
    ]
  ],
  "openalex": "W7202378733",
  "pdf_url": "https://arxiv.org/pdf/2608.11637",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1fx7z1bee5v90.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2608.11637",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.11637"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Uniform Local Asymptotics for Lévy Processes with Subexponential Jumps",
  "title_text": "Uniform Local Asymptotics for Lévy Processes with Subexponential Jumps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/1fx7z1bee5v90",
  "venue": "arXiv",
  "versions": []
}