{
  "abstract": "For one-dimensional strict local martingales of the form $\\mathrm{d} X_t=σ(X_t) \\mathrm{d} W_t$ starting from $X_{0}=x_{0}>0$, we prove the strong rate $\\mathbb{E}\\left[|X^h_N-X_T|\\right] \\lesssim h^{\\min\\{θα,\\frac{1}{2}\\}}$ for a discrete scheme~$X^h$ truncated at a level $h^{-α}$, with time step~$h$, as $h\\downarrow 0$, where~$θ$ depends on the truncation property. For the CEV model $σ(x)\\equiv x^{1+γ}$ in particular, the rate is~$\\frac{1}{2}$ for any $γ\\in (0,1)$ (up to a logarithmic pre-factor at $γ=\\frac{1}{2}$).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39896",
  "author_total": 1,
  "authors": [
    {
      "name": "Antoine Jacquier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fm74d73qs38ah.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39896",
  "fulltext_url": null,
  "id": "fm74d73qs38ah",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39896",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "q-fin.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39896",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fm74d73qs38ah.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39896",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39896"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Strong rate for one-dimensional driftless continuous strict local martingales",
  "title_text": "Strong rate for one-dimensional driftless continuous strict local martingales",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/fm74d73qs38ah",
  "venue": "arXiv",
  "versions": []
}