{
  "abstract": "This paper uses a generalized trivial coupling method to study the weak convergence of Stratonovich stochastic differential equations (SDEs) in high-dimensional environments. In contrast to standard methods that depend on the invertibility of the diffusion matrix or are restricted to low dimensions, our methodology deals with degenerate and non-invertible systems in arbitrary dimensions. We develop a theoretical framework for weak approximation, establishing the weak order of convergence under standard regularity assumptions. The method is integrated with multi-level Monte Carlo (MLMC) techniques to achieve optimal computational complexity O(ϵ−2) for mean square error ϵ2. We provide a detailed analysis of the variance decay, proving that Vℓ=O(δℓ2) for the coupled estimator, which leads to optimal complexity. Representative numerical tests on a 4-dimensional non-invertible system validate the theoretical results, proving the usefulness of the suggested approach. The numerical results demonstrate the computing benefits of the multi-level technique in high dimensions and validate the theoretical convergence rates. By offering both theoretical insights and useful computational methods for high-dimensional stochastic systems, this work advances the expanding field of computational stochastic analysis.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia",
    "Department of Statistics and Operations Research, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Yousef Alnafisah"
    },
    {
      "affs": [
        1
      ],
      "name": "M. A. Sohaly",
      "orcid": "0000-0001-5971-0048"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/erxzw4waz8prr.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203760",
  "fulltext_url": null,
  "id": "erxzw4waz8prr",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3760",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7222578209",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/erxzw4waz8prr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203760",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3760"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Stratonovich SDEs in High Dimensions: Weak Convergence Approach to Generalized Trivial Coupling",
  "title_text": "Stratonovich SDEs in High Dimensions: Weak Convergence Approach to Generalized Trivial Coupling",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/erxzw4waz8prr",
  "venue": "Mathematics",
  "versions": []
}