{
  "abstract": "The elephant random walk (ERW) is a discrete-time random walk with complete memory. At every step the walker chooses one of the previous increments at random and then either repeats with a constant probability $p\\in [0,1]$ or reverses it. Since its introduction by Schütz and Trimper, the model has become a useful probabilistic framework for studying long-range dependence, anomalous diffusion, reinforcement, and phase transitions. This paper proposes a generalized ERW model with time-dependent memory. In this generalized model, the usual constant memory parameter $p$ in the standard ERW is allowed to change with time. The cental limit theorems, and the law of the iterated logarithm and some other strong laws are obtained.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16065",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiequan Fan"
    },
    {
      "name": "Yongcheng Qi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/afpwve860f1nn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16065",
  "fulltext_url": null,
  "id": "afpwve860f1nn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16065",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7221816295",
  "pdf_url": "https://arxiv.org/pdf/2610.16065",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/afpwve860f1nn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16065",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16065"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A Generalized Elephant Random Walk with Time-Dependent Memory",
  "title_text": "A Generalized Elephant Random Walk with Time-Dependent Memory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/afpwve860f1nn",
  "venue": "arXiv",
  "versions": []
}