Random walks in cones revisited

Abstract

In this paper we continue our study of a multidimensional random walk with zero mean and finite variance killed on leaving a cone. We suggest a new approach that allows one to construct a positive harmonic function in Lipschitz cones under minimal moment conditions. This approach allows one also to obtain more accurate information about the behaviour of the harmonic function not far from the boundary of the cone. We also prove limit theorems under new moment conditions.