{
  "abstract": "We study fluctuation limit of a slow-fast system driven by $α$-stable Lévy noise with $1<α<2.$ The slow component is generated by an odd polynomial function $f(y):=y^q,$ while in the fast component, the drift is $g(y):=-|y|^p\\operatorname{sgn}(y)$ for some $p>0.$ Although the noise is given, the fluctuation limit is either a stable process or a Brownian motion, depending on both $p$ and $α.$ The critical line between stable limit and Brownian limit is $q+1-p=α/2.$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09906",
  "author_total": 3,
  "authors": [
    {
      "name": "Qingming Zhao"
    },
    {
      "name": "Xueru Liu"
    },
    {
      "name": "Wei Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6kh30mgpc7ey3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09906",
  "fulltext_url": null,
  "id": "6kh30mgpc7ey3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09906",
  "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",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7212192590",
  "pdf_url": "https://arxiv.org/pdf/2609.09906",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6kh30mgpc7ey3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09906",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09906"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Stable and Gaussian Fluctuation Limit of a Lévy-Driven Slow-Fast System with Polynomial Dissipation",
  "title_text": "Stable and Gaussian Fluctuation Limit of a Lévy-Driven Slow-Fast System with Polynomial Dissipation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/6kh30mgpc7ey3",
  "venue": "arXiv",
  "versions": []
}