{
  "abstract": "We study null controllability of backward stochastic heat systems with constant couplings in both the state and the martingale integrand, common scalar diffusion, and a localized drift control. We prove that null controllability is equivalent to a noncommutative word-rank condition on the two coupling matrices and the control matrix. The proof combines a factorization of the dual dynamics, positivity and small-time coercivity of a finite-dimensional stochastic Gramian, and a Lebeau--Robbiano spectral argument. Failure of the rank condition yields an invariant unobservable subspace.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.01836",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohamed Fadili"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bvbq350n24xjy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.01836",
  "fulltext_url": null,
  "id": "bvbq350n24xjy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.01836",
  "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"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7172435890",
  "pdf_url": "https://arxiv.org/pdf/2608.01836",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bvbq350n24xjy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2608.01836",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.01836"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A noncommunicative Kalman condition for null controllability of backward stochastic parabolic systems",
  "title_text": "A noncommunicative Kalman condition for null controllability of backward stochastic parabolic systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/bvbq350n24xjy",
  "venue": "arXiv",
  "versions": []
}