Recurrent random walks in nonnegative matrices II

Summary In this paper, we continue the study undertaken in our earlier paper M1]. One of the main results here can be described as follows. LetX ₀,X ₁, ... be a sequence of iid random affine maps from (R ⁺) ^d into itself. Let us write:W _n X _n X _n –1...X ₀ andZ _n X ₀ X ₁...X _n , where composition of maps is the rule of multiplication. By the attractorA(u),u(R ⁺) ^d , we mean the setA u={y(R⁺)^d:P(W_n uN i.o.) > 0 for every openN containingy}. It is shown that the attractorA(u), under mild conditions, is the support of a stationary probability measure, when the random walk (Z _n ) has at least one recurrent state.