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2014 Green's functions of random walks on the upper half plane
Kôhei Uchiyama
Tohoku Math. J. (2) 66(2): 289-307 (2014). DOI: 10.2748/tmj/1404911864

Abstract

We obtain an asymptotic estimate of the Green function of a random walk on $\boldsymbol{Z}^2$ having zero mean and killed when it exits from the upper half plane. A little more than the second moment condition is assumed. The estimate obtained is used to derive an exact asymptotic form of the hitting distribution of the lower half plane of the walk. The higher dimensional walks are dealt with in the same way.

Citation

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Kôhei Uchiyama. "Green's functions of random walks on the upper half plane." Tohoku Math. J. (2) 66 (2) 289 - 307, 2014. https://doi.org/10.2748/tmj/1404911864

Information

Published: 2014
First available in Project Euclid: 9 July 2014

zbMATH: 1296.60119
MathSciNet: MR3229598
Digital Object Identifier: 10.2748/tmj/1404911864

Subjects:
Primary: 60G50
Secondary: 60J45

Rights: Copyright © 2014 Tohoku University

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Vol.66 • No. 2 • 2014
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