We study the recurrence of homogeneous and oscillating random walks on the integers, simplifying former works of Spitzer and Kemperman, respectively. We add general remarks and discuss some links with renewal theory.

The paper is concerned with a new approach for the recurrence property of the oscillating process on Z in Kemperman’s sense. In the case when the random walk is ascending on Z− and descending on Z+,… Expand

Here 0 is the identi ty element of the (additive) group g~, #~0> is the probabili ty measure all of whose mass is concentrated at O, #~1~=# and #~> is the n-fold convolution of # with itself. Roughly… Expand

This textbook provides a systematic treatment of denumerable Markov chains, covering both the foundations of the subject and topics in potential theory and boundary theory. It is a discussion of… Expand

We establish a recurrence criterion for a model of inhomogeneous random walk in Z in environment stratified by parallel affine hyperplanes. The asymptotics of the random walk is governed by some… Expand

We give a recurrence criterion for a model of planar random walk in environment invariant under horizontal translations. Some examples are next developed, for instance when the environment is… Expand

Simple random walks on various types of partially horizontally oriented regular lattices are considered. The horizontal orientations of the lattices can be of various types (deterministic or random)… Expand