# 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.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [3 references]

https://hal.inria.fr/hal-01194687
Contributor : Coordination Episciences Iam <>
Submitted on : Monday, September 7, 2015 - 12:51:10 PM
Last modification on : Tuesday, September 3, 2019 - 12:28:04 PM
Long-term archiving on: : Tuesday, December 8, 2015 - 1:02:37 PM

### File

dmAI0115.pdf
Publisher files allowed on an open archive

### Identifiers

• HAL Id : hal-01194687, version 1

### 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. ⟨hal-01194687⟩

Record views