Exponential decay of random correlations for random Anosov systems mixing on fibers

Abstract: In this paper, we study the statistical property of Anosov systems on surface driven by an external force. By utilizing the Birkhoff cone method, we show that if the systems on surface satisfying the Anosov and topological mixing on fibers property, then the quenched random correlation for Holder observables with respect to the unique random SRB measures decays exponentially.