Green's functions of random walks on the upper half plane

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.