We study the path behavior of the symmetric walk on some special comb-type subsets of Z 2 which are obtained from Z 2 by generalizing the comb having ﬁnitely many horizontal lines instead of one.

We analyze the differences between the horizontal and the vertical component of the simple random walk on the 2-dimensional comb. In particular we evaluate by combinatorial methods the asymptotic… Expand

We study the path behavior of the anisotropic random walk on the two-dimensional lattice $$\mathbb {Z}^2$$ Z 2 . Simultaneous strong approximation of its components are given.

A random walk on a two-dimensional lattice with homogeneous rows and inhomogeneous columns, which could serve as a model for the study of some transport phemonema, is discussed. Subject to an… Expand

In the present work the results of K. L. Chung [2] concerning the maximum partial sums of sequences of independent random variables are obtained for a weaker condition. The method employed in the… Expand