{
  "abstract": "Fractional Brownian motion provides a useful framework for modeling random phenomena with anti-persistent temporal correlations that arise in applications such as anomalous diffusion, hydrology, finance, and geophysical processes. In this paper, we study a class of semilinear stochastic partial differential equations driven by additive fractional Brownian motion with Hurst parameter $H\\in(0,\\frac12)$. We establish the well-posedness and space-time regularity of the mild solution and investigate the strong convergence of a stochastic exponential integrator for the temporal discretization. The analysis allows the linear operator to be non-self-adjoint and combines analytic semigroup estimates with the canonical Hilbert-space structure associated with fractional Brownian motion and Malliavin calculus to handle the low temporal regularity of the noise. We derive an $H$-dependent strong temporal convergence rate, which reaches $H+\\frac12$ under maximal spatial regularity. Numerical experiments for a stochastic advection--diffusion--reaction problem with heterogeneous Darcy flow confirm the theoretical temporal convergence rates. We also estimate the mean of the solution with different Hurst parameters $H\\in(0,\\frac12)$ using the Monte Carlo method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02412",
  "author_total": 3,
  "authors": [
    {
      "name": "Antoine Tambue"
    },
    {
      "name": "Aurelien Junior Noupelah"
    },
    {
      "name": "Louis Aime Fono"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/02y3zmb7vgd9g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02412",
  "fulltext_url": null,
  "id": "02y3zmb7vgd9g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02412",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2612|Numerical methods for differential equations"
    ]
  ],
  "openalex": "W7220380263",
  "pdf_url": "https://arxiv.org/pdf/2610.02412",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/02y3zmb7vgd9g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02412",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02412"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Strong error analysis of a stochastic exponential integrator for SPDEs driven by fractional Brownian motion with H<1/2",
  "title_text": "Strong error analysis of a stochastic exponential integrator for SPDEs driven by fractional Brownian motion with H<1/2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/02y3zmb7vgd9g",
  "venue": "arXiv",
  "versions": []
}