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            <title xml:lang="en">The oscillating random walk on Z</title>
            <title xml:lang="fr">Sur la marche aléatoire oscillante sur Z</title>
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                <forename>Tran Duy</forename>
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            <idno type="stamp" n="UNIV-TOURS">Université François Rabelais</idno>
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            <idno type="stamp" n="UNIV-ORLEANS">Université d'Orléans</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="IDP">Institut Denis Poisson</idno>
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              <p>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.</p>
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