The Oscillating Random Walk on $$ {\mathbf {\mathbb {Z}}} $$ Z

Tran Duy Vo ()
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Tran Duy Vo: Université de Tours, Université d’Orléans, CNRS

Journal of Theoretical Probability, 2023, vol. 36, issue 4, 2426-2447

Abstract: Abstract The paper is concerned with a new approach for the recurrence properties of the oscillating random walk on $$\mathbb {Z}$$ Z in the sense of Kemperman. In the case when the random walk is ascending on $$\mathbb {Z}^-$$ Z - and descending on $$\mathbb {Z}^+$$ Z + , the invariant measure of the embedded process of successive crossing times is explicitly determined, which yields a sufficient condition for recurrence. Finally, we make use of this result to show that the general oscillating random walk is recurrent under some moment assumptions.

Keywords: Random walk; Markov chain; Irreducible class; Invariant measure; 60G50; 60J05; 60J10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-023-01250-z

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