{
  "abstract": "We bridge the gap between the mixed-moment theory of càdlàg rough stochastic differential equations (short:RSDEs), introduced by Friz, Hocquet and Lê (2021) and extended to the càdlàg setting by Allan and Pieper (2026), and the theory of rough semimartingales (short:RSMs), introduced by Friz and Zorin-Kranich (2023), by investigating the intersection of these two theories for the first time. By introducing the concept of good solutions to RSDEs, solutions which are simultaneously both mixed-moment solutions and RSMs, we develop a solution concept, which allows for good control on both moment-based and pathwise properties of solutions. The well-posedness of good solutions is proven using a fixed point argument on the space of $L^{2}$-martingales by suitably leveraging previously known mixed-moment estimates. Based on these insights we further characterize a large class of good solutions of semi-linear RSDEs through a novel rough stochastic Duhamel's principle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41664",
  "author_total": 3,
  "authors": [
    {
      "name": "Jannis R. Dause"
    },
    {
      "name": "Peter K. Friz"
    },
    {
      "name": "Jost Pieper"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/68km2gsgj0qyt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41664",
  "fulltext_url": null,
  "id": "68km2gsgj0qyt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41664",
  "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.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41664",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/68km2gsgj0qyt.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41664",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41664"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Bridging rough stochastic differential equations and rough semimartingales",
  "title_text": "Bridging rough stochastic differential equations and rough semimartingales",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/68km2gsgj0qyt",
  "venue": "arXiv",
  "versions": []
}