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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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Cited literature [3 references]

https://hal.inria.fr/hal-01194687
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Submitted on : Monday, September 7, 2015 - 12:51:10 PM
Last modification on : Tuesday, September 3, 2019 - 12:28:04 PM
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dmAI0115.pdf
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### Citation

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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