{
  "abstract": "We study a mixed regular--singular control problem for stochastic evolution equations in a Hilbert space with possibly unbounded random linear operators, a nonconvex regular-control domain, and a state-dependent singular coefficient. The singular control is an adapted nondecreasing càdlàg process whose terminal value need not be bounded. We prove well-posedness and weighted moment estimates for the forward and backward equations, and characterize the second-order adjoint by a conditionally expected operator-valued backward stochastic integral equation. An Itô-type formula for the quadratic form of this adjoint, together with spike and convex variations, yields a second-order Hamiltonian condition for the regular control, as well as nonnegativity and a contact condition for the optional singular Hamiltonian.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01545",
  "author_total": 3,
  "authors": [
    {
      "name": "Ying Hu"
    },
    {
      "name": "Guomin Liu"
    },
    {
      "name": "Shanjian Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e89kqw0e2cv16.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01545",
  "fulltext_url": null,
  "id": "e89kqw0e2cv16",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01545",
  "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.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7215887254",
  "pdf_url": "https://arxiv.org/pdf/2610.01545",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e89kqw0e2cv16.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.01545",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01545"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Vector- and operator-valued backward stochastic equations with finite-variation drivers and a maximum principle for singular stochastic control in infinite dimensions",
  "title_text": "Vector- and operator-valued backward stochastic equations with finite-variation drivers and a maximum principle for singular stochastic control in infinite dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/e89kqw0e2cv16",
  "venue": "arXiv",
  "versions": []
}