{
  "abstract": "We consider the estimation of drift, diffusion, and noise covariance from discrete observations of stochastic differential equations driven by Gaussian processes. For a fixed observation horizon $T>0$ and a known initial state $x_0\\in\\mathbb R$, we study \\begin{equation*} dX_t=a(X_t)\\,dt+σ(X_t)\\,dZ_t^{β,f}, \\qquad X_0=x_0,\\quad 0\\leq t\\leq T. \\end{equation*} \\smallskip\\noindent Here $a:\\mathbb R\\to\\mathbb R$ is the drift coefficient, $σ:\\mathbb R\\to(0,\\infty)$ is the diffusion coefficient, and $Z^{β,f}$ is a centered Gaussian process from the weighted sub-fractional Brownian family, with covariance \\begin{equation*} \\operatorname{Cov}(Z_s^{β,f},Z_t^{β,f}) =\\int_0^{s\\wedge t} f(r)q_β(s-r,t-r)\\,dr, \\qquad 0\\leq s,t\\leq T. \\end{equation*} \\smallskip\\noindent Here $s\\wedge t=\\min\\{s,t\\}$. The temporal weight $f:[0,T]\\to[0,\\infty)$ is measurable, bounded, and positive almost everywhere, and $β\\in(0,2)$ is the covariance exponent. For $u,v\\geq0$, the kernel is $q_β(u,v)=[u^β+v^β-(u+v)^β]/(1-β)$ when $β\\ne1$. Its continuous extension at $β=1$ is $q_1(u,v)=(u+v)\\log(u+v)-u\\log u-v\\log v$, with $0\\log0=0$. Using the Euler approximation, we reconstruct the Gaussian driving increments from observed transitions and use their joint density to obtain a trajectory likelihood. Neural and radial-basis representations model the drift, diffusion, and normalized temporal weight, while a likelihood profile estimates the covariance exponent and diffusion scale. We compare the method with two neural alternatives on the same simulated trajectories in twenty coefficient settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00793",
  "author_total": 1,
  "authors": [
    {
      "name": "J. H. Ramirez-Gonzalez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0bpq1mtvaegy4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00793",
  "fulltext_url": null,
  "id": "0bpq1mtvaegy4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00793",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7216482009",
  "pdf_url": "https://arxiv.org/pdf/2610.00793",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0bpq1mtvaegy4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:14Z",
      "native_id": "2610.00793",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00793"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Inference for stochastic differential equations driven by weighted sub-fractional Brownian motion using neural networks and the Euler approximation",
  "title_text": "Inference for stochastic differential equations driven by weighted sub-fractional Brownian motion using neural networks and the Euler approximation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:14Z",
  "url": "https://research.draconitic.com/paper/0bpq1mtvaegy4",
  "venue": "arXiv",
  "versions": []
}