{
  "abstract": "We study the rough differential equation $$ \\frac{du_t}{dt}= F(u_t) ζ_t, \\ \\ u(0) = u_0 \\in \\mathbb{R}^d, $$ where $F : \\mathbb{R}^d \\to L(\\mathbb{R}^d, \\mathbb{R}^d)$ is a sufficiently regular vector field, and the noise $ζ$ is a distribution in $\\mathscr{C}^{α-1}(\\mathbb{R})$ for $α\\in (\\frac{1}{4}, \\frac{1}{3})$. We construct solutions to this equation at lower regularity than previous work of Gubinelli-Imkeller-Perkowski and Prömel-Trabs using ideas from the high-order paracontrolled viewpoint of Bailleul-Bernicot. The key tool in our work is the development of a harmonic-analytic framework for proving a set of iterated commutator estimates which are necessary for the solution theory. We also show the procedure of enhancement when the noise $ζ= dZ$, where $Z$ is a realization of fractional Brownian motion with Hurst parameter $H \\in (\\frac{1}{4}, \\frac{1}{3})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17307",
  "author_total": 1,
  "authors": [
    {
      "name": "Tim Van Hoose"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6c02ctf472961.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17307",
  "fulltext_url": null,
  "id": "6c02ctf472961",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17307",
  "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.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7221806616",
  "pdf_url": "https://arxiv.org/pdf/2610.17307",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6c02ctf472961.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.17307",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17307"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Higher-Order Paracontrolled Calculus for Geometric Rough Paths",
  "title_text": "Higher-Order Paracontrolled Calculus for Geometric Rough Paths",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/6c02ctf472961",
  "venue": "arXiv",
  "versions": []
}