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ISSN 1088-6850(e) ISSN 0002-9947(p)

The hitting distributions of a line for two dimensional random walks

Author(s): Kôhei Uchiyama
Journal: Trans. Amer. Math. Soc. 362 (2010), 2559-2588.
MSC (2010): Primary 60G50; Secondary 60J45
Posted: 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: 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
Posted: December 3, 2009
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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