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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Asymptotic results for the absorption times of random walks with a barrier


Author: Pavlo Negadaĭlov
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 79 (2008).
Journal: Theor. Probability and Math. Statist. 79 (2009), 127-138
MSC (2000): Primary 60J80, 60E99; Secondary 60G42
Published electronically: December 30, 2009
MathSciNet review: 2494542
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Abstract | References | Similar Articles | Additional Information

Abstract: A sequence $ R_k^{(n)}:=R_{k-1}^{(n)}+\xi_k1_{\left\{R_{k-1}^{(n)}+\xi_k<n\right\}}$, $ k\in\mathbf{N}$, $ R_0^{(n)}:=0$, is called a random walk with a barrier $ n \in \mathbf{N}$, where the $ \xi_k$ are independent copies of a random variable $ \xi$ assuming positive integer values. The asymptotic behavior of the absorption times is studied in the paper for a random walk with a barrier. This behavior depends on the properties of the tail of the distribution of the random variable $ \xi$.


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Additional Information

Pavlo Negadaĭlov
Affiliation: Faculty for Cybernetics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: npasha@ukr.net

DOI: http://dx.doi.org/10.1090/S0094-9000-09-00785-6
PII: S 0094-9000(09)00785-6
Keywords: Random walks with a barrier, absorption moments
Received by editor(s): October 18, 2007
Published electronically: December 30, 2009
Additional Notes: The research is supported by DFG, project 436UKR 113/93/0-1
Article copyright: © Copyright 2009 American Mathematical Society