Asymptotic results for the absorption times of random walks with a barrier
Author:
Pavlo Negadaĭlov
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 79 (2009), 127-138
MSC (2000):
Primary 60J80, 60E99; Secondary 60G42
DOI:
https://doi.org/10.1090/S0094-9000-09-00785-6
Published electronically:
December 30, 2009
MathSciNet review:
2494542
Full-text PDF Free Access
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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 $\xi$.
References
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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
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