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Non-uniform Berry-Esseen bounds for the elephant random walk with random step sizes

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

Abstract

In this paper, we consider the non-uniform normal approximations of the elephant random walk with random step sizes. When the random step sizes have finite moments of order 2+δ, δ ∈ (0, 1), or satisfy the Bernstein condition, we establish the non-uniform Berry-Esseen bounds. These results refine existing central limit theorems and uniform Berry-Esseen bounds for the elephant random walk. As a consequence, moderate deviation principles and local limit theorems are also obtained.

Suggested Citation

  • Huang, Xulan & Fan, Xiequan & Xiang, Kainan, 2026. "Non-uniform Berry-Esseen bounds for the elephant random walk with random step sizes," Stochastic Processes and their Applications, Elsevier, vol. 200(C).
    • Handle: RePEc:eee:spapps:v:200:y:2026:i:c:s0304414926001559
    DOI: 10.1016/j.spa.2026.105023
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