Suppose al, a2,... is a sequence of real numbers with a,, oo. If lim sup( Xl + + X, )/a,, = a a.s. for every sequence of independent nonnegative uniformly bounded random variables Xi, X2,... satisfying some hypothesis condition A, then for every (arbitrarily-dependent) sequence of nonnegative uniformly bounded random variables Y1, Y2,..., lim sup( Y, + + Y, )/a,, = a a.s. on the set where the c...

This paper considers the stability of moments of stochastic systems, such as stability of the mean or mean-square stability. The exponential growth behavior of moments is compared to almost sure exponential growth via Lyapunov exponents. We develop a series of indices that are useful to describe system performance under random perturbations. The theory is applied to two examples, including an e...