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

Abstract

Let $\mu^n$ be the distribution of a product of $n$ independent identically distributed random matrices. We study tightness and convergence of the sequence $\{\mu^n, n \geq 1\}$. 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.