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

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  • Kôhei Uchiyama

    (Tokyo Institute of Technology)

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.

Suggested Citation

  • Kôhei Uchiyama, 2016. "The Hitting Distribution of a Line Segment for Two-Dimensional Random Walks," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1661-1684, December.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:4:d:10.1007_s10959-015-0629-5
    DOI: 10.1007/s10959-015-0629-5
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    References listed on IDEAS

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    1. Kesten, Harry, 1987. "Hitting probabilities of random walks on," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 165-184.
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