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

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

2009-02-25

arxiv.org/abs/0902.4369v1

Mathematics

Probability

30 pages, 1 figure

Scientific paper

We study the path behaviour of a simple random walk on the 2-dimensional comb lattice ${\mathbb C}^2$ 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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