Abstract: | For a sequence T(1), T(2),…of piecewise monotonic C2 - transformations of the unit interval I onto itself, we prove exponential ψ- mixing, an almost Markov property and other higher-order mixing properties. Furthermore, we obtain optimal rates of convergence in the central limit Theorem and large deviation relations for the sequence fk oT(k?1)o…oT(1), k=1, 2, …, provided that the real-valued functions f1, f2,…on I are of bounded variation and the corresponding probability measure on I possesses a positive, Lipschitz-continuous Lebesgue density. |