On the limiting set of nonnegative matrix products

We study the asymptotic set and limiting behaviour of normed products of the form x(t) = x(o) H1H2...Ht/x(0) H1H2...Ht1 as t --> [infinity], where x(0) may be drawn from a closed set of (1 x n) stochastic vectors, and each Hi from a closed subset of (n x n) nonnegative matrices satisfying certain other conditions. The results extend to general nonnegative matrices, along the lines of [7], results for stochastic matrices Hi partly due to Hartfiel [3] and Stanford [8].