A central limit theorem for contractive stochastic dynamical systems

If (F-n)(n is an element of N) is a sequence of independent and identically distributed random mappings from a second countable locally compact state space X to X which itself is independent of the 3-valued initial variable X-0, the discrete-time stochastic process (X-n)(n greater than or equal to 0), defined by the recursion equation X-n = F-n(Xn-1) for n is an element of N, has the Markov property. Since X is Polish in particular, a complete metric d exists. The random mappings (F-n)(n is an element of N) are assumed to satisfy P-a.s. [GRAPHICS] Conditions on the distribution of l(F-n) are given for the existence of an invariant distribution of X-0 making the process (X-n)(n greater than or equal to 0) stationary and ergodic. Our main result corrects a central limit theorem by Loskot and Rudnicki [3] and removes an error in its proof. Instead of trying to compare the sequence phi(X-n)(n greater than or equal to 0) for some phi : X --> R with a triangular scheme of independent random variables our proof is based on an approximation by a martingale difference scheme.