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Journal of Theoretical Probability

, Volume 29, Issue 4, pp 1661–1684 | Cite as

The Hitting Distribution of a Line Segment for Two-Dimensional Random Walks

  • Kôhei Uchiyama
Article

Abstract

Asymptotic estimates of the hitting distribution of a long segment on the real axis for two-dimensional random walks on \(\mathbf{Z}^2\) of zero mean and finite variances are obtained: Some are general and exhibit its apparent similarity to the corresponding Brownian density, while others are so detailed as to involve certain characteristics of the random walk.

Keywords

Harmonic measure in a slit plane Line segment Asymptotic formula Random walk of zero mean and finite variances 

Mathematics Subject classification (2010)

Primary 60G50 Secondary 60J45 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsTokyo Institute of TechnologyMeguroJapan

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