{
  "abstract": "In this paper, we focuses on how the distribution of random step sizes affects Cramér-type moderate deviations and precise large deviations for the elephant random walk with random step sizes. First, with sub-exponential moment condition of random step sizes, we establish Cramér-type moderate deviation results. Consequently, moderate deviation principles are obtained. Secondly, for random step sizes with sub-exponential tails, we establish a large deviation principle on tail probabilities. Finally, for random step sizes with regularly varying tails, we obtain precise large deviations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26928",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiequan Fan"
    },
    {
      "name": "Shuyuan Liang"
    },
    {
      "name": "Dongxue Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f18ftbg25kbkr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26928",
  "fulltext_url": null,
  "id": "f18ftbg25kbkr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26928",
  "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",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7223085528",
  "pdf_url": "https://arxiv.org/pdf/2610.26928",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f18ftbg25kbkr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.26928",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26928"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Cramér-type moderate deviations and precise large deviations for the elephant random walk with random step sizes",
  "title_text": "Cramér-type moderate deviations and precise large deviations for the elephant random walk with random step sizes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/f18ftbg25kbkr",
  "venue": "arXiv",
  "versions": []
}