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2009 Strong Limit Theorems for a Simple Random Walk on the 2-Dimensional Comb
Endre Csáki, Miklós Csörgö, Antonia Feldes, Pál Révész
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Electron. J. Probab. 14: 2371-2390 (2009). DOI: 10.1214/EJP.v14-710


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.


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Endre Csáki. Miklós Csörgö. Antonia Feldes. Pál Révész. "Strong Limit Theorems for a Simple Random Walk on the 2-Dimensional Comb." Electron. J. Probab. 14 2371 - 2390, 2009.


Accepted: 1 November 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1190.60020
MathSciNet: MR2556015
Digital Object Identifier: 10.1214/EJP.v14-710

Primary: 60F17
Secondary: 60F15 , 60G50 , 60J10 , 60J65

Keywords: 2-dimensional comb , 2-dimensional Wiener process , iterated Brownian motion , Laws of the iterated logarithm , Random walk , strong approximation

Vol.14 • 2009
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