# 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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Communication dans un congrès
Roesler, Uwe. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, pp.243-250, 2008, DMTCS Proceedings
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https://hal.inria.fr/hal-01194687
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• HAL Id : hal-01194687, version 1

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Alex Iksanov, Pavlo Negadajlov. On the number of zero increments of random walks with a barrier. Roesler, Uwe. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, pp.243-250, 2008, DMTCS Proceedings. 〈hal-01194687〉

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