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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Csaki, Endre¹  Csoergo, Miklos²  Foeldes, Antonia³  Revesz, Pal⁴ 

[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

关键词: Random walk;    2-dimensional comb;    Strong approximation;    2-dimensional Wiener process;    Local time;    Laws of the iterated logarithm;    Iterated Brownian motion;   

DOI  :  10.1016/j.spa.2011.01.009

来源: Elsevier

【 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.

【 授权许可】

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