{
  "abstract": "Suppose $X=(X_t)_{t\\ge0}$ is a supercritical superprocess with a non-local branching mechanism on a Lusin space $E$, whose mean semigroup admits a positive leading eigenvalue $λ_1$ with a bounded positive eigenfunction $φ$ and a finite eigenmeasure $\\widetildeφ$. Let $Y_t:=\\int_0^t X_s\\mathrm{d}s$ be its occupation measure. We first prove a law of large numbers, that is, for every bounded measurable function $f$, $e^{-λ_1 t}\\langle f,Y_t\\rangle$ converges in $L^2$ to $λ_1^{-1}\\langle f,\\widetildeφ\\rangle W^φ_\\infty$, where $W^φ_\\infty$ is the limit of the martingale $W^φ_t:=e^{-λ_1 t}\\langleφ,X_t\\rangle$. We then establish functional central limit theorems for the fluctuations of $\\langle f,Y_t\\rangle$ around this random centering. We show that the normalisation and the limit are determined by the spectral decay rate of $f$ compared with the critical value $λ_1/2$, and there are three possible regimes: after suitable normalisation, the fluctuation process converges in distribution in $\\mathcal{C}[0,+\\infty)$ either to a mixed Gaussian process $\\sqrt{W^φ_{\\infty}}G(f)$, or to a constant Gaussian process with random variance depending on $W^φ_{\\infty}$, or to a non-Gaussian limit given by the limit of a martingale associated with the spectral projection of $f$. These results are the occupation-time counterparts of the fluctuation theorems for instantaneous linear functionals of supercritical non-local branching superprocesses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12503",
  "author_total": 1,
  "authors": [
    {
      "name": "Ting Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/63w5zz1kr9mbc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12503",
  "fulltext_url": null,
  "id": "63w5zz1kr9mbc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12503",
  "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": "W7221548098",
  "pdf_url": "https://arxiv.org/pdf/2610.12503",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/63w5zz1kr9mbc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.12503",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12503"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Functional limit theorems for weighted occupation times of supercritical superprocesses",
  "title_text": "Functional limit theorems for weighted occupation times of supercritical superprocesses",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/63w5zz1kr9mbc",
  "venue": "arXiv",
  "versions": []
}