{
  "abstract": "We consider a stochastic parabolic equation on the $n$-dimensional flat torus $\\mathbb{T}^n=(\\mathbb{R}/(2π\\mathbb Z))^n$, $n\\in\\mathbb N$, whose only control acts in the drift. The multiplicative-noise coefficient is adapted and may depend jointly on the sample point, time, and space. Its spatial profiles are assumed to be real analytic with a uniform positive radius of analyticity, while the corresponding analytic norm is only required to be square integrable in time, uniformly along sample paths. We prove a state-only observability inequality with an $L^1$-in-time mean-square observation norm and deduce null controllability from every measurable spatial set of positive measure by one adapted drift control. The same one-time interpolation estimate also yields approximate controllability to arbitrary square-integrable random terminal targets. The proof is based on a direct analytic energy estimate for the adjoint state, followed by propagation of smallness and a telescoping argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28937",
  "author_total": 2,
  "authors": [
    {
      "name": "Qi Lü"
    },
    {
      "name": "Yu Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/31bfn636apnym.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28937",
  "fulltext_url": null,
  "id": "31bfn636apnym",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28937",
  "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.OC"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7214324497",
  "pdf_url": "https://arxiv.org/pdf/2609.28937",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/31bfn636apnym.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28937",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28937"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Null Controllability of a Stochastic Parabolic Equation with a Space-Dependent Analytic Noise Coefficient",
  "title_text": "Null Controllability of a Stochastic Parabolic Equation with a Space-Dependent Analytic Noise Coefficient",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/31bfn636apnym",
  "venue": "arXiv",
  "versions": []
}