Stochastic stability of invariant subspaces

We prove that a relevant part of the Lyapunov spectrum and the correspondin g Oseledets spaces of a quasi-compact linear cocycle are stable under a cer tain type of random perturbation. The basic approach is a graph-transform a rgument. The result applies to the spectrum of (not necessarily i.i.d.) ran domly perturbed expanding maps and yields generalizations of results recent ly obtained by Baladi, Kondah and Schmitt [5] with different methods.