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

[41] ON THE RATE OF CONVERGENCE IN THE CENTRAL-LIMIT-THEOREM FOR WEAKLY DEPENDENT RANDOM-VARIABLES
ZUPAROV, TM
THEORY OF PROBABILITY AND ITS APPLICATIONS, 1991, 36 (04) : 783 - 792
[42] On the Convergence Rate in a Local Renewal Theorem for a Random Markov Walk
Bakai, G. A.
MATHEMATICAL NOTES, 2024, 115 (3-4) : 479 - 488
[43] A bound on the rate of convergence in the central limit theorem for renewal processes under second moment conditions
Reinert, G.
Yang, C.
JOURNAL OF APPLIED PROBABILITY, 2020, 57 (01) : 343 - 360
[44] On the rate of convergence in the global central limit theorem for random sums of uniformly strong mixing random variables
Sunklodas, Jonas Kazys
LITHUANIAN MATHEMATICAL JOURNAL, 2020, 60 (03) : 410 - 423
[45] On the rate of convergence in the global central limit theorem for random sums of uniformly strong mixing random variables
Jonas Kazys Sunklodas
Lithuanian Mathematical Journal, 2020, 60 : 410 - 423
[46] ON NONUNIFORM CONVERGENCE RATE ESTIMATES IN THE CENTRAL LIMIT THEOREM
Nefedova, Yu. S.
Shevtsova, I. G.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2013, 57 (01) : 28 - 59
[47] CHARACTERIZING THE RATE OF CONVERGENCE IN THE CENTRAL LIMIT-THEOREM
HALL, P
ANNALS OF PROBABILITY, 1980, 8 (06): : 1037 - 1048
[48] ON THE RATE OF CONVERGENCE IN THE CENTRAL LIMIT-THEOREM FOR SEMIMARTINGALES
LIPTSER, RS
SHIRYAEV, AN
THEORY OF PROBABILITY AND ITS APPLICATIONS, 1983, 27 (01) : 1 - 13
[49] ON THE RATE OF CONVERGENCE IN THE CENTRAL LIMIT THEOREM FOR HIERARCHICAL LAPLACIANS
Bendikov, Alexander
Cygan, Wojciech
ESAIM-PROBABILITY AND STATISTICS, 2019, 23 : 68 - 81
[50] A note on the rate of convergence in the Boolean central limit theorem
Salazar, Mauricio
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2023,

← 1 2 3 4 5 →