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

Alex Iksanov; Pavlo Negadajlov

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

Alex Iksanov ¹ Pavlo Negadajlov ¹

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 : absorption time recursion with random indices random walk undershoot

Type de document :

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

Domaine :

Informatique [cs] / Mathématique discrète [cs.DM]

Mathématiques [math] / Systèmes dynamiques [math.DS]

Mathématiques [math] / Combinatoire [math.CO]

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https://hal.inria.fr/hal-01194687
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