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The oscillating random walk on Z

Sur la marche aléatoire oscillante sur Z

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1
D T Vo
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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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Dates and versions

hal-03510517 , version 1 (04-01-2022)

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