MIXING PROPERTIES AND CENTRAL-LIMIT-THEOREM FOR CLASS OF NONIDENTICALPIECEWISE MONOTONIC C-2-TRANSFORMATIONS

For a sequence T-(1), T-(2),... of piecewise monotonic C-2-transformat ions of the unit interval I onto itself, we prove exponential psi-mixi ng, an almost Markov property and other higher-order mixing properties . Furthermore, we obtain optimal rates of convergence in the central l imit theorem and large deviation relations for the sequence f(k)oT((k- 1)) o ... oT((1)), k = 1, 2,..., provided that the real-valued functio ns f(1), f(2),... on I are Of bounded variation and the corresponding probability measure on I possesses a positive, Lipschitz-continuous Le besgue density.