The Green Functions of Two Dimensional Random Walks Killed on a Line and their Higher Dimensional Analogues

Kohei Uchiyama (Tokyo Institute of Technology)

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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Pages: 1161-1189

Publication Date: May 19, 2010

DOI: 10.1214/EJP.v15-793

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