• Corpus ID: 245704294

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

  title={The oscillating random walk on \$\mathbb\{Z\}\$},
  author={Dl Vo},
  • D. Vo
  • Published 5 January 2022
  • Mathematics
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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