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.
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