Tightness of Products of Random Matrices and Stability of Linear Stochastic Systems

Abstract

Let μn be the distribution of a product of n independent identically distributed random matrices. We study tightness and convergence of the sequence {μn, n ≥ 1}. We apply this to linear stochastic differential (and difference) equations, characterize the stability in probability, in the sense of Hashminski, of the zero solution, and find all their stationary solutions.