{
  "abstract": "We study the backward-Euler scheme for a class of stochastic functional differential equations (SFDEs) with memory driven by a fractional Brownian motion with Hurst parameter H > 1/2. We first establish the local consistency of the method, with a local truncation error of order H -ρ- β + 1, and then, as the main result, prove the uniform global pathwise convergence of the numerical approximation, on a set of probability one, with order H -ρ -β, for β ∈ (1-H, 1/2) and 0 < ρ < H -β. A uniform high-probability formulation with deterministic constants follows as a corollary. In particular, the convergence order can be taken arbitrarily close to 2H -1, matching the order obtained for the explicit Euler scheme. The convergence proof relies on an exact integral representation of the scheme at mesh points, an a priori bound for the numerical solution, fractional calculus estimates, and a Gronwall inequality for weakly singular kernels.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37019",
  "author_total": 4,
  "authors": [
    {
      "name": "Alexander Abreu"
    },
    {
      "name": "Lisandro Fermin"
    },
    {
      "name": "Ernesto Mordecki"
    },
    {
      "name": "Soledad Torres"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ddj18ygm8zc1w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37019",
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  "id": "ddj18ygm8zc1w",
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  "landing_url": "https://hal.science/hal-05768392v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
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      "openalex",
      "2612|Numerical methods for differential equations"
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  "openalex": "W7214985612",
  "pdf_url": "https://hal.science/hal-05768392/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ddj18ygm8zc1w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:42Z",
      "native_id": "hal-05768392",
      "source": "hal",
      "url": "https://hal.science/hal-05768392v1"
    },
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37019",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37019"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Consistency and Convergence of the Backward-Euler Scheme for Stochastic Functional Differential Equations Driven by Fractional Brownian Motion",
  "title_text": "Consistency and Convergence of the Backward-Euler Scheme for Stochastic Functional Differential Equations Driven by Fractional Brownian Motion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/ddj18ygm8zc1w",
  "venue": "HAL",
  "versions": []
}