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arXiv · 2610.26928

Cramér-type moderate deviations and precise large deviations for the elephant random walk with random step sizes

Xiequan Fan·Shuyuan Liang·Dongxue Ma
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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.

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Xiequan Fan, Shuyuan Liang, Dongxue Ma. 2026-10-17. Cramér-type moderate deviations and precise large deviations for the elephant random walk with random step sizes. https://arxiv.org/abs/2610.26928

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