Rate of moment convergence in the central limit theorem for the elephant random walk

被引：1

作者：

Hayashi, Masafumi ^{[1
]}

Oshiro, So ^{[2
]}

Takei, Masato ^{[3
]}

机构：

[1] Univ Ryukyus, Dept Math Sci, Okinawa, Japan

[2] Univ Ryukyus, Grad Sch Engn & Sci, Dept Math Sci, Okinawa, Japan

[3] Yokohama Natl Univ, Fac Engn, Dept Appl Math, Yokohama, Japan

来源：

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT | 2023年 / 2023卷 / 02期

关键词：

self-interacting random walks; random walk with memory; step reinforcement; elephant random walk; limit theorems; asymptotic normality;

D O I：

10.1088/1742-5468/acb265

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

The one-dimensional elephant random walk is a typical model of discrete-time random walk with step-reinforcement, and is introduced by Schutz and Trimper (2004 Phys. Rev. E 70 045101). It has a parameter alpha & ISIN;(-1,1) alpha = 0 corresponds to the simple symmetric random walk, and when alpha > 0 (resp. alpha < 0), the mean displacement of the walker at time n grows (resp. vanishes) like n ( alpha ). The walk admits a phase transition at alpha=1/2

引用

页数：24

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