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 barrierConference paper

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) behaviour of Vn 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 Vn 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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