Baladi V., Viana M. Strong stochastic stability and rate of mixing for unimodal maps (120K, AMS TeX) ABSTRACT. We consider small random perturbations of a large class of nonuniformly hyperbolic unimodal maps and prove stochastic stability in the strong sense (L^1-convergence of invariant densities) and uniform bounds for the exponential rate of decay of correlations. Our method is based on an analysis of the spectrum of a modified Perron-Frobenius operator for a tower extension of the Markov chain.