Stochastic stability of Lyapunov exponents and Oseledets splittings for semi-invertible matrix cocycles

摘要

We establish (i) stability of Lyapunov exponents and (ii) convergence inprobability of Oseledets spaces for semi-invertible matrix cocycles, subjectedto small random perturbations. The first part extends results of Ledrappier andYoung to the semi-invertible setting. The second part relies on the study ofevolution of subspaces in the Grassmannian.