{
  "abstract": "We develop an intrinsic well-posedness theory for nonlinear backward stochastic differential equations (BSDEs) driven simultaneously by Brownian motion and a (level-$2$) rough path of finite $p$-variation. Unlike earlier approaches based on smooth approximation or transformation methods, we formulate the equation directly by viewing its solution as a rough semimartingale (in the sense of \\cite{friz2023rough}). This framework is particularly suited to BSDEs, whose Brownian martingale component is only implicitly defined and lacks the \\emph{a priori} time regularity required by stochastic-sewing-based controlled rough path methods \\cite{fhl21,allan2024rough}. We establish comparison, existence, uniqueness, and stability under the natural regularity condition $H\\in C_b^γ$, $γ>p$. The main analytical difficulty, namely, the loss of integrability arising from nonlinear composition, is overcome through conditional $p$-variation norms with BMO-type properties. Finally, by randomizing the rough driver as a Brownian rough path, we establish a direct correspondence between rough BSDEs and backward doubly stochastic differential equations (BDSDEs).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06606",
  "author_total": 4,
  "authors": [
    {
      "name": "Peter K. Friz"
    },
    {
      "name": "Jian Song"
    },
    {
      "name": "Huilin Zhang"
    },
    {
      "name": "Kuan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5sazrxcj71tb2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06606",
  "fulltext_url": null,
  "id": "5sazrxcj71tb2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06606",
  "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",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7212047551",
  "pdf_url": "https://arxiv.org/pdf/2609.06606",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5sazrxcj71tb2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.06606",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06606"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Rough backward stochastic differential equations",
  "title_text": "Rough backward stochastic differential equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/5sazrxcj71tb2",
  "venue": "arXiv",
  "versions": []
}