{
  "abstract": "We bound the difference between two stochastic Volterra processes with identical Lipschitz coefficients but different kernels. For non-convolution kernels, we establish estimates in $C^0([0,T];L^p(Ω))$, $p\\geq 2$, and for convolution kernels in $L^p(Ω;L^q(0,T))$, $q \\in [1,p]$, and $C^β([0,T];L^p(Ω))$, $L^p(Ω;C^β([0,T]))$, where the range of the Hölder exponent $β\\in (0,1]$ is the maximal permitted by the regularity of the processes. For the fractional kernel, we then construct Markovian approximations whose error we show to decay as $e^{-a\\sqrt{N}}$ in the aforementioned norms, using an $N$-node quadrature based on sinc methods. Numerical experiments for the fractional Brownian motion verify our findings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17472",
  "author_total": 3,
  "authors": [
    {
      "name": "Noé Corneille"
    },
    {
      "name": "Kristin Kirchner"
    },
    {
      "name": "Pietro Pezzoli Frigerio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3dj5v8w6cfzsx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17472",
  "fulltext_url": null,
  "id": "3dj5v8w6cfzsx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17472",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7213421733",
  "pdf_url": "https://arxiv.org/pdf/2609.17472",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3dj5v8w6cfzsx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17472",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17472"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Convergence in Hölder norms for Markovian approximations of stochastic Volterra equations",
  "title_text": "Convergence in Hölder norms for Markovian approximations of stochastic Volterra equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/3dj5v8w6cfzsx",
  "venue": "arXiv",
  "versions": []
}