{
  "abstract": "In this paper, we prove pathwise uniform convergence at rates up to $1/2$ for tamed exponential Euler schemes for semilinear hyperbolic stochastic evolution equations with superlinearly growing nonlinearities and multiplicative noise. We take the term hyperbolic to mean that the leading operator generates a contractive $C_0$-semigroup but no parabolic smoothing occurs. Under local Lipschitz, polynomial growth, coercivity, and monotonicity conditions on the nonlinearities, we establish pathwise uniform strong error estimates of the form \\begin{equation*} \\Big(\\mathbb{E}\\max_{0\\le j \\le N} \\|U(t_j)-U^j\\|_X^p\\Big)^{1/p} \\lesssim \\sqrt{k} \\end{equation*} on a Hilbert space $X$ for $p\\in [2,\\infty)$. Here, $U$ is the mild solution and $U^j$ is the tamed exponential Euler approximation at time $t_j=jk$ with step size $k>0$. This extends previous convergence results for non-parabolic SPDEs from globally to locally Lipschitz nonlinearities, allowing both drift and diffusion to grow polynomially. In a stochastic Kato framework, we further establish local and global well-posedness as well as uniform a priori estimates for the mild solution and its approximation. Applications to nonlinear stochastic transport, Airy, wave-type, and dissipatively damped nonlinear Schrödinger equations are included, covering different nonlinearities-stopped and fractionally tamed schemes. For the Klein-Gordon equation with cubic velocity damping, this complements previous results obtained for additive noise.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08872",
  "author_total": 1,
  "authors": [
    {
      "name": "Katharina Klioba"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3mgkj41g9mg1f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08872",
  "fulltext_url": null,
  "id": "3mgkj41g9mg1f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08872",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "2612|Numerical methods for differential equations"
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  "openalex": "W7212059947",
  "pdf_url": "https://arxiv.org/pdf/2609.08872",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3mgkj41g9mg1f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.08872",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08872"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Strong convergence rates of tamed exponential Euler schemes for superlinear hyperbolic SPDEs",
  "title_text": "Strong convergence rates of tamed exponential Euler schemes for superlinear hyperbolic SPDEs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/3mgkj41g9mg1f",
  "venue": "arXiv",
  "versions": []
}