Stochastic Stability for Fiber Expanding Maps via a Perturbative Spectral Approach

Abstract

We consider small perturbations of expanding maps induced by skew-product mappings whose base dynamics are not invertible necessarily. Adopting a previously developed perturbative spectral approach, we show stability of the densities of the unique absolutely continuous invariant probability measures for expanding maps under these perturbations, and upper bounds on the rate of exponential decay of fiber correlations associated to the measures as the noise level goes to zero.