当前位置: X-MOL 学术J. Stat. Mech. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Cramr moderate deviations for the elephant random walk
Journal of Statistical Mechanics: Theory and Experiment ( IF 2.4 ) Pub Date : 2021-02-11 , DOI: 10.1088/1742-5468/abd942
Xiequan Fan 1 , Haijuan Hu 2 , Xiaohui Ma 1
Affiliation  

We establish some limit theorems for the elephant random walk (ERW), including Berry–Esseen’s bounds, Cramr 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.



中文翻译:

大象随机行走的Cramr中度偏差

我们为大象随机游走(ERW)建立了一些极限定理,包括Berry–Esseen的边界,Cramr中等偏差和局部极限定理。这些极限定理可以看作是ERW中心极限定理的改进。此外,通过这些极限定理,我们得出结论,正态近似的收敛速度和正态分布的吸引域主要取决于介于0和3/4之间的存储参数p

更新日期:2021-02-11
down
wechat
bug