ELEPHANT RANDOM WALKS WITH DELAYS

被引：0

作者：

Gut, Allan ^{[1
]}

Stadtmueller, Ulrich ^{[2
]}

机构：

[1] Uppsala Univ, Dept Math, Box 480, SE-75106 Uppsala, Sweden

[2] Ulm Univ, Dept Number Theory & Probabil Theory, D-89069 Ulm, Germany

来源：

REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES | 2022年 / 67卷 / 1-2期

关键词：

Elephant random walk; delay; law of large numbers; asymptotic (non)normality; law of iterated logarithm; difference equation; Markov chain;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the simple random walk the steps are independent, that is., the walker has no memory. In contrast, in the elephant random walk (ERW), which was introduced by Schutz and Trimper [9] in 2004, the next step always depends on the whole path so far. One extension, as suggested recently by Bercu et al. [2], is to allow for delays, that is, to put mass at zero. Our aim is to extend results for the ordinary ERW to elephant random walks with delays (ERWD).

引用

页码：51 / 66

页数：16

共 50 条

[41] Random vicious walks and random matrices
Baik, J
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2000, 53 (11) : 1385 - 1410
[42] ON THE RANGE OF RANDOM WALKS IN RANDOM ENVIRONMENT
ZHOU XIANYIN(Department of Mathematics
Chinese Annals of Mathematics, 1995, (01) : 131 - 138
[43] RANDOM-WALKS IN A RANDOM ENVIRONMENT
SOLOMON, F
ANNALS OF PROBABILITY, 1975, 3 (01): : 1 - 31
[44] Random walks in a sparse random environment
Matzavinos, Anastasios
Roitershtein, Alexander
Seol, Youngsoo
ELECTRONIC JOURNAL OF PROBABILITY, 2016, 21
[45] Random Walks in Cooling Random Environments
Avena, Luca
den Hollander, Frank
SOJOURNS IN PROBABILITY THEORY AND STATISTICAL PHYSICS - III: INTERACTING PARTICLE SYSTEMS AND RANDOM WALKS, A FESTSCHRIFT FOR CHARLES M. NEWMAN, 2019, 300 : 23 - 42
[46] THE EXTREMES OF RANDOM WALKS IN RANDOM SCENERIES
Franke, Brice
Saigo, Tatsuhiko
ADVANCES IN APPLIED PROBABILITY, 2009, 41 (02) : 452 - 468
[47] Random Walks in Hypergraph
Bellaachia, Abdelghani
Al-Dhelaan, Mohammed
INTERNATIONAL JOURNAL OF EDUCATION AND INFORMATION TECHNOLOGIES, 2021, 15 : 13 - 20
[48] On subordinate random walks
Mimica, Ante
FORUM MATHEMATICUM, 2017, 29 (03) : 653 - 664
[49] Hipster random walks
L. Addario-Berry
H. Cairns
L. Devroye
C. Kerriou
R. Mitchell
Probability Theory and Related Fields, 2020, 178 : 437 - 473
[50] The art of random walks
Telcs, Andras
ART OF RANDOM WALKS, 2006, 1885 : 1 - +

← 1 2 3 4 5 →