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

@misc{fan2026cramértype,
  title = {{Cramér-type moderate deviations and precise large deviations for the elephant random walk with random step sizes}},
  author = {Xiequan Fan and Shuyuan Liang and Dongxue Ma},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26928},
  eprint = {2610.26928},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26928},
}

TY  - UNPB
TI  - Cramér-type moderate deviations and precise large deviations for the elephant random walk with random step sizes
AU  - Xiequan Fan
AU  - Shuyuan Liang
AU  - Dongxue Ma
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.26928
UR  - https://arxiv.org/abs/2610.26928
AB  - 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.
ER  -