{
  "abstract": "For $z\\in\\mathbb{R}$ we reconsider the solution $f_z$ to the standard normal Stein equation, corresponding to the Kolmogorov distance for distributions on the real line. More precisely, we prove the Lipschitz continuity of the related function $x\\mapsto ρ_z(x):=xf_z(x)$ and explain how this observation may help to remove some unnecessary technical conditions from recent Berry-Esseen bounds in the literature around the Malliavin-Stein method. We further show that the Lipschitz constants of the functions $ρ_z$ are yet not uniformly bounded in $z$ and discuss consequences of this negative result.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25992",
  "author_total": 1,
  "authors": [
    {
      "name": "Christian Döbler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/604b5r7fdr67e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25992",
  "fulltext_url": null,
  "id": "604b5r7fdr67e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25992",
  "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",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7223026332",
  "pdf_url": "https://arxiv.org/pdf/2610.25992",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/604b5r7fdr67e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25992",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25992"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A note on the solution to the standard normal Stein equation",
  "title_text": "A note on the solution to the standard normal Stein equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/604b5r7fdr67e",
  "venue": "arXiv",
  "versions": []
}