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On the number of zero increments of random walks with a barrier

Abstract : Continuing the line of research initiated in Iksanov and Möhle (2008) and Negadajlov (2008) we investigate the asymptotic (as $n \to \infty$) behaviour of $V_n$ the number of zero increments before the absorption in a random walk with the barrier $n$. In particular, when the step of the unrestricted random walk has a finite mean, we prove that the number of zero increments converges in distribution. We also establish a weak law of large numbers for $V_n$ under a regular variation assumption.
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Alex Iksanov, Pavlo Negadajlov. On the number of zero increments of random walks with a barrier. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. pp.243-250, ⟨10.46298/dmtcs.3568⟩. ⟨hal-01194687⟩

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