{
  "abstract": "We study a nonlocal stochastic optimal control problem in which the control acts through the elliptic smoothing operator $\\mathcal{S}=(I-Δ)^{-1}$ on $\\mathbb{R}^d$. The state is described by the law of a controlled diffusion, equivalently by a controlled Fokker-Planck equation with coefficients depending on $\\mathcal{S}u$. We prove the existence of an optimal control by the direct method in the calculus of variations. We then derive a Pontryagin-type maximum principle by spike variations, relying on sharp properties of the operator $\\mathcal{S}$. The result yields a pointwise minimisation rule for the optimal control. We discuss the meaning of the optimal control problem in the case of population dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10029",
  "author_total": 2,
  "authors": [
    {
      "name": "Stefana-Lucia Anita"
    },
    {
      "name": "Luca Di Persio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ff8z0sx82pbf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10029",
  "fulltext_url": null,
  "id": "1ff8z0sx82pbf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10029",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.10029",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ff8z0sx82pbf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10029",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10029"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Nonlocal Stochastic Optimal Control with Elliptic-Type Smoothing",
  "title_text": "A Nonlocal Stochastic Optimal Control with Elliptic-Type Smoothing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/1ff8z0sx82pbf",
  "venue": "arXiv",
  "versions": []
}