Cramer moderate deviations for the elephant random walk

被引：10

作者：

Fan, Xiequan ^{[1
]}

Hu, Haijuan ^{[2
]}

Ma, Xiaohui ^{[1
]}

机构：

[1] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China

[2] Northeastern Univ Qinhuangdao, Sch Math & Stat, Qinhuangdao, Hebei, Peoples R China

来源：

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT | 2021年 / 2021卷 / 02期

基金：

中国国家自然科学基金;

关键词：

stochastic processes; large deviation;

D O I：

10.1088/1742-5468/abd942

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

We establish some limit theorems for the elephant random walk (ERW), including Berry-Esseen's bounds, Cramer moderate deviations and local limit theorems. These limit theorems can be regarded as refinements of the central limit theorem for the ERW. Moreover, by these limit theorems, we conclude that the convergence rate of normal approximations and the domain of attraction of normal distribution mainly depend on a memory parameter p which lies between 0 and 3/4.

引用

页数：20

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