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arXiv · 2003.12937

Cram\'{e}r moderate deviations for the elephant random walk

Xiequan Fan·Haijuan Hu·Xiaohui Ma
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Abstract

We establish some limit theorems for one-dimensional elephant random walk, including Berry-Esseen bounds, Cram\'{e}r moderate deviations and local limit theorems. These limit theorems can be regarded as refinements of the central limit theorems for the elephant random walk. Moreover, by these limit theorems, we conclude that the domain of attraction of normal distribution mainly depends on a memory parameter $p$ which lies between $0$ and $3/4.$

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Xiequan Fan, Haijuan Hu, Xiaohui Ma. 2020-03-29. Cram\'{e}r moderate deviations for the elephant random walk. https://arxiv.org/abs/2003.12937

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