{
  "abstract": "We study parabolic stochastic partial differential equations on metric measure spaces $(\\mathbb{X}, d,m)$ of the form $$ \\partial_t u(t,x) = \\mathcal{L}^* u(t,x) + b(t,x,u(t,x)) + σ(t,x,u(t,x)) \\dot{W}(t,x),\\quad t>0,\\, x \\in \\mathbb X, $$ where $\\mathcal{L}$ is the generator of a Markov process which possesses transition densities, and $\\dot{W}$ is a Gaussian noise that is white in time and possibly with spatial correlation. We assume the coefficients $b$ and $σ$ are Lipschitz and satisfy the linear growth condition. We formulate general and checkable assumptions on $(\\mathbb{X},\\mathcal{L},\\dot{W})$ that ensure existence and uniqueness of probabilistically strong, continuous, tempered mild solutions. We then prove comparison principles (including a strong comparison principle) and strict positivity, relative to initial conditions. Our framework allows non-symmetric heat kernels and includes diffusion-type and stable-type examples, such as metric graphs and fractal spaces with sub-Gaussian heat kernel estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07790",
  "author_total": 4,
  "authors": [
    {
      "name": "Louis Wai-Tong Fan"
    },
    {
      "name": "Zhenyao Sun"
    },
    {
      "name": "Johnny"
    },
    {
      "name": "Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/epytq0hzkpy9w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07790",
  "fulltext_url": null,
  "id": "epytq0hzkpy9w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07790",
  "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",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221052669",
  "pdf_url": "https://arxiv.org/pdf/2610.07790",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/epytq0hzkpy9w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07790",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07790"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Comparison principles for stochastic reaction-diffusion equations on metric measure spaces",
  "title_text": "Comparison principles for stochastic reaction-diffusion equations on metric measure spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/epytq0hzkpy9w",
  "venue": "arXiv",
  "versions": []
}