Cram\'{e}r moderate deviations for the elephant random walk
Probability
2023-10-03 v2
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 which lies between and
Cite
@article{arxiv.2003.12937,
title = {Cram\'{e}r moderate deviations for the elephant random walk},
author = {Xiequan Fan and Haijuan Hu and Xiaohui Ma},
journal= {arXiv preprint arXiv:2003.12937},
year = {2023}
}