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<p>For the elephant random walk, namely, the elephant random walk with deterministic step sizes, rates of moment convergence have been obtained by Hayashi, Oshiro and Takei [J. Stat. Mech. Theory Exp., 2023]. In this paper, we extend above results to the elephant random walk with random step sizes, namely, we obtained rates of moment convergence for the position of the walker when memory parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \in (-1, 1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Moment Convergence Rate of Elephant Random Walk with Random Step Sizes

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Xulan Huang,
  • Xiequan Fan,
  • Chao Liu,
  • Kainan Xiang

摘要

For the elephant random walk, namely, the elephant random walk with deterministic step sizes, rates of moment convergence have been obtained by Hayashi, Oshiro and Takei [J. Stat. Mech. Theory Exp., 2023]. In this paper, we extend above results to the elephant random walk with random step sizes, namely, we obtained rates of moment convergence for the position of the walker when memory parameter \(\alpha \in (-1, 1)\) α ∈ ( - 1 , 1 ) .