On the local time of random walk on the 2-dimensional comb

被引：11

作者：

Csaki, Endre ^{[1
]}

Csoergo, Miklos ^{[2
]}

Foeldes, Antonia ^{[3
]}

Revesz, Pal ^{[4
]}

机构：

[1] Hungarian Acad Sci, Alfred Renyi Inst Math, H-1364 Budapest, Hungary

[2] Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada

[3] CUNY Coll Staten Isl, Dept Math, Staten Isl, NY 10314 USA

[4] Vienna Univ Technol, Inst Stat & Wahrscheinlichkeitstheorie, A-1040 Vienna, Austria

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2011年 / 121卷 / 06期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Random walk; 2-dimensional comb; Strong approximation; 2-dimensional Wiener process; Local time; Laws of the iterated logarithm; Iterated Brownian motion; BROWNIAN-MOTION; INCREMENTS; THEOREMS; SITES; BIG; LAW;

D O I：

10.1016/j.spa.2011.01.009

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study the path behaviour of general random walks, and that of their local times, on the 2-dimensional comb lattice C-2 that is obtained from Z(2) by removing all horizontal edges off the x-axis. We prove strong approximation results for such random walks and also for their local times. Concentrating mainly on the latter, we establish strong and weak limit theorems, including Strassen-type laws of the iterated logarithm, Hirsch-type laws, and weak convergence results in terms of functional convergence in distribution. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：1290 / 1314

页数：25

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