{
  "abstract": "A control variate method was introduced by Garnier and Mertz (2022) for multivalued stochastic differential equations driven by colored noise. For smooth observables, the asymptotic variance is $O(\\varepsilon^{2})$, where $\\varepsilon^{2}$ is the correlation time of the noise. However, for non-smooth reliability observables, such as threshold indicators and overshoot severities, rate estimates have not been established in general. In this paper, rate estimates are derived for the inertial dry-friction inclusion driven by colored noise in the three regimes whose white-noise propagators are known. The asymptotic variance of the resulting control variate estimators is $O(\\varepsilon^{2α})$ for $α$-Hölder observables with $α\\in(0,1]$, $O(\\varepsilon)$ for observables of bounded variation satisfying a one-sided continuity condition, $O(\\varepsilon^{1+α})$ for observables that are both $α$-Hölder and of bounded variation, and $O(\\varepsilon^{\\min\\{2,1+2α\\}})$ for observables with finitely many $α$-cusps, where $α\\in (0, 1]$ is the cusp exponent. The last three bounds hold up to logarithmic factors. Bounds on the bias of the white-noise approximation and non-asymptotic sample-size estimates are also derived, and the comparison principle is shown to be preserved under coupled time discretization. Numerical experiments in the three regimes support the predicted rates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27765",
  "author_total": 1,
  "authors": [
    {
      "name": "Lihong Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/44v21frw3skpb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27765",
  "fulltext_url": null,
  "id": "44v21frw3skpb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27765",
  "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.ST"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1804|Probabilistic and Robust Engineering Design"
    ]
  ],
  "openalex": "W7223097013",
  "pdf_url": "https://arxiv.org/pdf/2610.27765",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/44v21frw3skpb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27765",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27765"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Control variates for dry friction under colored noise: variance rates for non-smooth observables",
  "title_text": "Control variates for dry friction under colored noise: variance rates for non-smooth observables",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:13Z",
  "url": "https://research.draconitic.com/paper/44v21frw3skpb",
  "venue": "arXiv",
  "versions": []
}