Alex Iksanov ; Pavlo Negadajlov - On the number of zero increments of random walks with a barrier

dmtcs:3568 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science - https://doi.org/10.46298/dmtcs.3568
On the number of zero increments of random walks with a barrierArticle

Authors: Alex Iksanov 1; Pavlo Negadajlov 1

  • 1 Faculty of Cybernetics [Kyiv]

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.


Volume: DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: absorption time,recursion with random indices,random walk,undershoot,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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