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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The hitting distributions of a line for two dimensional random walks


Author: Kôhei Uchiyama
Journal: Trans. Amer. Math. Soc. 362 (2010), 2559-2588
MSC (2010): Primary 60G50; Secondary 60J45
Published electronically: December 3, 2009
MathSciNet review: 2584611
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Abstract: For every irreducible random walk on $ \mathbf{Z}^2$ with zero mean and finite $ 2+\delta$ absolute moment ( $ 0\leq \delta <1$) we obtain fine asymptotic estimates of the probability that the first visit of the walk to the horizontal axis takes place at a specified site of it.


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Additional Information

Kôhei Uchiyama
Affiliation: Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro Tokyo 152-8551, Japan
Email: uchiyama@math.titech.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-09-05072-7
PII: S 0002-9947(09)05072-7
Keywords: First visited site, asymptotic formula, Fourier analysis, random walk of zero mean and finite variances
Received by editor(s): March 28, 2008
Published electronically: December 3, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.