Analysis of random walks on a hexagonal lattice

被引：9

作者：

Di Crescenzo, Antonio ^{[1
]}

Macci, Claudio ^{[2
]}

Martinucci, Barbara ^{[1
]}

Spina, Serena ^{[1
]}

机构：

[1] Univ Salerno, Dipartimento Matemat, Via Giovanni Paolo II 132, I-84084 Fisciano, SA, Italy

[2] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Sci, I-00133 Rome, Italy

来源：

IMA JOURNAL OF APPLIED MATHEMATICS | 2019年 / 84卷 / 06期

关键词：

random walk; hexagonal lattice; probability generating function; large deviations; moderate deviations; first-passage time; MODEL; SEQUENCES;

D O I：

10.1093/imamat/hxz026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a two-dimensional Brownian motion is also discussed. Furthermore, we obtain some results on its asymptotic behaviour making use of large deviation theory. Finally, we investigate the first-passage-time problem of the random walk through a vertical straight line. Under suitable symmetry assumptions, we are able to determine the first-passage-time probabilities in a closed form, which deserve interest in applied fields.

引用

页码：1061 / 1081

页数：21