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

共 50 条

[21] On the rate of convergence in the global central limit theorem for random sums of independent random variables
Sunklodas, Jonas Kazys
LITHUANIAN MATHEMATICAL JOURNAL, 2017, 57 (02) : 244 - 258
[22] Exact Convergence Rate of the Local Limit Theorem for a Branching Random Walk in Zd with a Random Environment in Time
Liu, Jian-xin
Gao, Zhi-qiang
CHINESE ANNALS OF MATHEMATICS SERIES B, 2024, 45 (05) : 805 - 822
[23] Exact convergence rate of the central limit theorem and polynomial convergence rate for branching processes in a random environment
Li, Yingqiu
Zhang, Xin
Lu, Zhan
Xiao, Sheng
STATISTICS & PROBABILITY LETTERS, 2025, 216
[24] CENTRAL LIMIT THEOREM FOR RANGE OF TRANSIENT RANDOM WALK
JAIN, NC
PRUITT, WE
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 76 (04) : 758 - &
[25] On the rate of convergence of Lp norms in the central limit theorem for independent random variables
Sunklodas J.
Lithuanian Mathematical Journal, 2002, 42 (3) : 296 - 307
[26] Exact convergence rate in the central limit theorem for a branching process in a random environment
Gao, Zhi-Qiang
STATISTICS & PROBABILITY LETTERS, 2021, 178
[27] On the rate of convergence in the martingale central limit theorem
Mourrat, Jean-Christophe
BERNOULLI, 2013, 19 (02) : 633 - 645
[28] On the rate of convergence in the entropic central limit theorem
Artstein, S
Ball, KM
Barthe, F
Naor, A
PROBABILITY THEORY AND RELATED FIELDS, 2004, 129 (03) : 381 - 390
[29] Improvement of convergence rate estimates in the central limit theorem under weakened moment conditions
V. Yu. Korolev
S. V. Popov
Doklady Mathematics, 2012, 86 : 506 - 511
[30] ON RATE OF CONVERGENCE IN MULTIDIMENSIONAL CENTRAL LIMIT THEOREM
SAZANOV, VV
THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1967, 12 (01): : 77 - &

← 1 2 3 4 5 →