Strong stochastic stability and rate of mixing for unimodal maps

Abstract

Let I be a compact real interval and f:{I}\to {I} be a unimodalmap with negative Schwarzian derivative and nondegenerate critical point.Then under certain further assumptions the authors show that these maps arestable under random perturbations of the map -- in the sense of L_1convergence of invariant densities of the associated Markov chain (strongstochastic stability). The authors also give uniform bounds for theexponential rate of decay of correlations.