  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.
