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. LetX₀,X₁, ... be a sequence of iid random affine maps from (R⁺)^d into itself. Let us write:W_nX_nX_n–1...X₀ andZ_nX₀X₁...X_n, where composition of maps is the rule of multiplication. By the attractorA(u),u(R⁺)^d, we mean the setAu={y(R⁺)^d:P(W_nuN 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.