# The oscillating random walk on $\mathbb{Z}$

@inproceedings{Vo2022TheOR, title={The oscillating random walk on \$\mathbb\{Z\}\$}, author={Dl Vo}, year={2022} }

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+, we determine the invariant measure of the embedded process of successive crossing times and then prove a necessary and sufficient condition for recurrence. Finally, we make use of this result to show that the general oscillating process is recurrent under some Hölder-typed moment assumptions.

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