Geodesic
On the number of zero increments of random walks with a barrier
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science (2008).

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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. 
@article{DMTCS_2008_special_254_a14,
     author = {Iksanov, Alex and Negadajlov, Pavlo},
     title = {On the number of zero increments of random walks with a barrier},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science},
     year = {2008},
     doi = {10.46298/dmtcs.3568},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3568/}
}
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Iksanov, Alex; Negadajlov, Pavlo. On the number of zero increments of random walks with a barrier. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science (2008). doi : 10.46298/dmtcs.3568. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3568/

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