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 Electronic Journal of Probability > Vol. 14 (2009) > Paper 82 open journal systems 


Strong limit theorems for a simple random walk on the 2-dimensional comb

Endre Csáki, A. Rényi Institute, Hungary
Miklós Csörgő, Carleton University, Ottawa, Canada
Antónia Földes, College of Staten Island, CUNY, New York
Pál Révész, Technical University, Vienna, Austria


Abstract
We study the path behaviour of a simple random walk on the 2-dimensional comb lattice C2 that is obtained from Z2 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.


Full text: PDF

Pages: 2371-2390

Published on: November 1, 2009
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Electronic Journal of Probability. ISSN: 1083-6489