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

D Vo

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arXiv · 2201.01515

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

D Vo

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Abstract

The paper is concerned with a new approach for the recurrence property of the oscillating process on $\mathbb{Z}$ in Kemperman's sense. In the case when the random walk is ascending on $\mathbb{Z}^-$ and descending on $\mathbb{Z}^+$, 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 H{\"o}lder-typed moment assumptions.

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D Vo. 2022-01-05. The oscillating random walk on $\mathbb{Z}$. https://arxiv.org/abs/2201.01515

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