{
  "abstract": "We show that purely continuous microscopic diffusions can homogenize to a Markov process with genuine jumps. Consider a multiscale diffusion with time-dependent generator $\\mathcal{L}_{0}+r_{t}^ε\\mathcal{L}_{1}$ driven by a regenerative random environment. When the integrated activity over a regeneration cycle has a regularly varying tail of index $β\\in(0,1)$, the cumulative operational clock converges to a $β$-stable subordinator, compressing finite activity-driven diffusion into vanishingly short physical time intervals. To overcome the noncommutativity of $\\mathcal{L}_0$ and $\\mathcal{L}_1$, we develop an extended-time parametrization paired with Khasminskii-type time discretization, establishing finite-dimensional convergence and strong semigroup convergence on $C_{0}(\\mathbb{R}^{d})$ toward a jump process with nonlocal generator $\\overline{\\mathcal{L}}=\\mathcal{L}_{0}-κ(-\\mathcal{L}_{1})^β$. Under uniform ellipticity of $\\mathcal{L}_{1}$, the fractional power $(-\\mathcal{L}_{1})^β$ is identified as a $2β$-stable-like nonlocal operator. We also clarify physical-time path-topology obstructions and apply the framework to Poisson resetting pulses, Ornstein--Uhlenbeck diffusions, and multiscale stochastic volatility.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20302",
  "author_total": 1,
  "authors": [
    {
      "name": "Qi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/487fznp5mey2z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20302",
  "fulltext_url": null,
  "id": "487fznp5mey2z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20302",
  "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",
      "1703|Advanced Mathematical Modeling in Engineering"
    ]
  ],
  "openalex": "W7222238795",
  "pdf_url": "https://arxiv.org/pdf/2610.20302",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/487fznp5mey2z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20302",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20302"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Jump limits of continuous multiscale diffusions: Homogenization under heavy-tailed activity bursts",
  "title_text": "Jump limits of continuous multiscale diffusions: Homogenization under heavy-tailed activity bursts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/487fznp5mey2z",
  "venue": "arXiv",
  "versions": []
}