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2010 The Green Functions of Two Dimensional Random Walks Killed on a Line and their Higher Dimensional Analogues
Kohei Uchiyama
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Electron. J. Probab. 15: 1161-1189 (2010). DOI: 10.1214/EJP.v15-793

Abstract

We obtain asymptotic estimates of the Green functions of random walks on the two-dimensional integer lattice that are killed on the horizontal axis. A basic asymptotic formula whose leading term is virtually the same as the explicit formula for the corresponding Green function of Brownian motion is established under the existence of second moments only. Some refinement of it is given under a slightly stronger moment condition. The extension of the results to random walks on the higher dimensional lattice is also given.

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Kohei Uchiyama. "The Green Functions of Two Dimensional Random Walks Killed on a Line and their Higher Dimensional Analogues." Electron. J. Probab. 15 1161 - 1189, 2010. https://doi.org/10.1214/EJP.v15-793

Information

Accepted: 19 May 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1226.60069
MathSciNet: MR2659761
Digital Object Identifier: 10.1214/EJP.v15-793

Subjects:
Primary: 60G50

Keywords: absorption on a line , Asymptotic formula , Green function , random walk of zero mean and finite variances

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Vol.15 • 2010
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