{
  "abstract": "We establish quantitative weak convergence for the joint terminal law of the solution to a stochastic wave equation and the normalized error of its exponential Euler approximation. For multiplicative trace-class noise and spatial regularity $α\\in(1,2]$, the normalized error converges to its limiting distribution at rate $O(m^{-(α-1)})$, where $m$ is the number of time steps. This estimate identifies the leading weak bias and yields a first-order weak-error expansion with remainder $O(m^{-α})$. Moreover, by canceling the leading weak-error term, we construct a Richardson extrapolation scheme with weak convergence order $α$ for $α\\in(1,2]$ and show that this rate is sharp. To overcome the lack of parabolic smoothing and control the remainders amplified by normalization, we combine dimension-uniform regularity estimates for the joint Kolmogorov equation with a conditional weak expansion and backward transport of coefficient directions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16896",
  "author_total": 4,
  "authors": [
    {
      "name": "Jianbo Cui"
    },
    {
      "name": "Diancong Jin"
    },
    {
      "name": "Huagui Liu"
    },
    {
      "name": "Derui Sheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d8zk2gtg2s28z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16896",
  "fulltext_url": null,
  "id": "d8zk2gtg2s28z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16896",
  "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"
    ],
    [
      "openalex",
      "2612|Numerical methods for differential equations"
    ]
  ],
  "openalex": "W7221753131",
  "pdf_url": "https://arxiv.org/pdf/2610.16896",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d8zk2gtg2s28z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:16Z",
      "native_id": "2610.16896",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16896"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Quantitative asymptotic error analysis and Richardson extrapolation for exponential Euler approximations of stochastic wave equations",
  "title_text": "Quantitative asymptotic error analysis and Richardson extrapolation for exponential Euler approximations of stochastic wave equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:16Z",
  "url": "https://research.draconitic.com/paper/d8zk2gtg2s28z",
  "venue": "arXiv",
  "versions": []
}