{
  "abstract": "In this article, we construct, for a broad class of one-dimensional stochastic reaction-diffusion equations, a sequence of spatially-structured individual-based models whose rescaled empirical processes converge to the solution of the equation. The purpose of this article is to show that, whenever the rescaled one-step mean and variance of a reasonable individual-based model converge to those of an SDE with drift $b(x)x(1-x)+θ^+(1-x)-θ^-x$ and noise coefficient $\\sqrt{σ(x)x(1-x)}$, under certain moment conditions there also exists a corresponding multi-island model, composed of independent and identically distributed copies of the individual-based model on each island, with selection and mutation scaled to the diffusive time scale, coupled through migration, which converges to an SPDE with a Laplacian plus the same drift and noise coefficients, provided this SPDE is unique in law.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02669",
  "author_total": 3,
  "authors": [
    {
      "name": "Adrián González Casanova"
    },
    {
      "name": "Johnny"
    },
    {
      "name": "Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dcya6rkwx5vsb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02669",
  "fulltext_url": null,
  "id": "dcya6rkwx5vsb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02669",
  "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",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7220381249",
  "pdf_url": "https://arxiv.org/pdf/2610.02669",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dcya6rkwx5vsb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02669",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02669"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "From Individual-Based Models to General Stochastic Reaction Diffusion Equations",
  "title_text": "From Individual-Based Models to General Stochastic Reaction Diffusion Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/dcya6rkwx5vsb",
  "venue": "arXiv",
  "versions": []
}