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

Kôhei Uchiyama ()
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Kôhei Uchiyama: Tokyo Institute of Technology

Journal of Theoretical Probability, 2016, vol. 29, issue 4, 1661-1684

Abstract: Abstract Asymptotic estimates of the hitting distribution of a long segment on the real axis for two-dimensional random walks on $$\mathbf{Z}^2$$ 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; Primary 60G50; Secondary 60J45 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-015-0629-5

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