The Oscillating Random Walk on Z

The paper is concerned with a new approach for the recurrence properties of the oscillating random walk on Z in the sense of Kemperman. In the case when the random walk is ascending on Z-and descending on Z(+), the invariant measure of the embedded process of successive crossing times is explicitly determined, which yields a sufficient condition for recurrence. Finally, we make use of this result to show that the general oscillating random walk is recurrent under some moment assumptions.