{
  "abstract": "This paper studies the convergence rate of the Polyak-Ruppert average estimator in one-dimensional linear stochastic approximation recursion driven by Markov chains, allowing the Markov chain to start from any initial distribution. Under the conditions of positive Harris recurrence, non-periodicity, and one-step domination, combined with the fourth-moment condition of the coefficient function with respect to the stationary distribution, this paper uses the exchangeable pair technique to prove that after deterministic bias correction for the average estimator, a Berry--Esseen bound of order $n^{-α/2}$ can be obtained, where the step size exponent is $α\\in (1/2, 1)$. Moreover, for the statistics without bias correction and after variance normalization, the asymptotic normal approximation error is asymptotically equivalent to a normal constant multiplied by $n^{1/2 - α}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35538",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhijun Cai"
    },
    {
      "name": "YUjie Qin"
    },
    {
      "name": "Zhuosong Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f7k5vayhrywm9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35538",
  "fulltext_url": null,
  "id": "f7k5vayhrywm9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35538",
  "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|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7223869883",
  "pdf_url": "https://arxiv.org/pdf/2610.35538",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f7k5vayhrywm9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35538",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35538"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Berry--Esseen bounds for stochastic approximation with Markovian noise",
  "title_text": "Berry--Esseen bounds for stochastic approximation with Markovian noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/f7k5vayhrywm9",
  "venue": "arXiv",
  "versions": []
}