{
  "abstract": "In this paper, we establish an $L^2$ maximal inequality for partial sums of Gaussian-subordinated random variables. More precisely, let $f:\\mathbb{R}\\to\\mathbb{R}$ belong to $L^2(γ)$ and have Hermite rank at least $d$, where $γ$ denotes the standard Gaussian measure. If the covariance matrix of the underlying Gaussian family, with standard normal marginals, satisfies a uniform $d$th-power row bound $K$, then the $L^2$ norm of the maximal partial sum is bounded by $C_{d,K}\\sqrt n\\,\\|f\\|_{L^2(γ)}$. The constant $C_{d,K}$ is independent of $(f,n)$ and depends on the covariance structure only through $K$. As a consequence, our $L^2$ maximal inequality controls Hermite tails uniformly in the path norm. In discrete time, this yields the Breuer--Major--Donsker principle under the sole finite-variance assumption, removing both the additional $L^{2+}$-integrability assumption of Nourdin and Nualart (Probab. Theory Related Fields, 2020) and the prediction-theoretic or decimation assumptions of Mansanarez, Poly, and Zheng (arXiv:2607.11469). In continuous time, we likewise obtain the Breuer--Major--Donsker principle under finite variance alone, removing the additional moment assumption of Campese, Nourdin, and Nualart (Ann. Probab., 2020). For the nonstationary self-similar setting considered there, we remove the same extra moment assumption in the subcritical regime, while a separate leading-chaos argument yields the corresponding logarithmically normalized critical limit. [Abstract shorten to meet arXiv requirement]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09404",
  "author_total": 2,
  "authors": [
    {
      "name": "Dionysis Milesis"
    },
    {
      "name": "Guangqu Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fcvczhkqa4xvb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09404",
  "fulltext_url": null,
  "id": "fcvczhkqa4xvb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09404",
  "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": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7220905100",
  "pdf_url": "https://arxiv.org/pdf/2610.09404",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fcvczhkqa4xvb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09404",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09404"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "$L^p$ maximal inequalities for Gaussian subordination with applications to Breuer--Major--Donsker principles",
  "title_text": "L^p maximal inequalities for Gaussian subordination with applications to Breuer--Major--Donsker principles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/fcvczhkqa4xvb",
  "venue": "arXiv",
  "versions": []
}