Lyapunov regularity for random dynamical systems

This paper is concerned with the Lyapunov regularity of linear random dynamical systems. Both continuous and discrete cases are treated and the conditions are expressed in terms of the so-called regularity coefficient, which is an essential element of the theory of Lyapunov forward regularity developed by Lyapunov himself. It turns out that, using the celebrated multiplicative ergodic theorem of Oseledets, the Lyapunov forward regularity is “typical” in a measure theoretical sense.