{
  "abstract": "Let an Itô semimartingale be observed at times satisfying $τ_{i+1}^n-τ_i^n=(nθ_{τ_i^n})^{-1}$, where $θ$ is adapted and càdlàg, and $θ$ and its reciprocal are bounded on compact intervals. Under the usual hypothesis (H) on the semimartingale, we prove fixed-time stable convergence for test functions whose Hessian is $o(\\norm{x})$ at zero. The limit is a sum of jump contributions with sampling scale $θ_{T-}^{-1}$ and separate pre-jump and post-jump volatilities. The proof establishes joint stable convergence of the local Poisson positions and Brownian increments on the endogenous grid, and controls infinitely many small jumps by a uniform Itô estimate. Three examples identify the left-limit sampling scale and show why positivity and càdlàg regularity alone cannot replace local control of the reciprocal sampling intensity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09570",
  "author_total": 1,
  "authors": [
    {
      "name": "Yi Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c5kh9k41afafx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09570",
  "fulltext_url": null,
  "id": "c5kh9k41afafx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09570",
  "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",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7220897324",
  "pdf_url": "https://arxiv.org/pdf/2610.09570",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c5kh9k41afafx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09570",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09570"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A fixed-time stable limit theorem for non-normalized functionals on irregular time grids",
  "title_text": "A fixed-time stable limit theorem for non-normalized functionals on irregular time grids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/c5kh9k41afafx",
  "venue": "arXiv",
  "versions": []
}