@article{EJP710,
author = {Endre Csáki and Miklós Csörgö and Antonia Feldes and Pál Révész},
title = {Strong Limit Theorems for a Simple Random Walk on the 2-Dimensional Comb},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {14},
year = {2009},
keywords = {Random walk; 2-dimensional comb; strong approximation; 2-dimensional Wiener process; iterated Brownian motion; Laws of the iterated logarithm},
abstract = {We study the path behaviour of a simple random walk on the $2$-dimensional comb lattice $C^2$ that is obtained from $\mathbb{Z}^2$ by removing all horizontal edges off the $x$-axis. In particular, we prove a strong approximation result for such a random walk which, in turn, enables us to establish strong limit theorems, like the joint Strassen type law of the iterated logarithm of its two components, as well as their marginal Hirsch type behaviour.},
pages = {no. 82, 2371-2390},
issn = {1083-6489},
doi = {10.1214/EJP.v14-710},
url = {http://ejp.ejpecp.org/article/view/710}}