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The oscillating random walk on Z

Abstract : 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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03510517
Contributor : Tran Duy Vo Connect in order to contact the contributor
Submitted on : Tuesday, January 4, 2022 - 3:13:19 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:36 PM

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  • HAL Id : hal-03510517, version 1
  • ARXIV : 2201.01515

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D Vo. The oscillating random walk on Z. 2022. ⟨hal-03510517⟩

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