If (F-n)(n is an element of N) is a sequence of independent and identi
cally distributed random mappings from a second countable locally comp
act state space X to X which itself is independent of the 3-valued ini
tial variable X-0, the discrete-time stochastic process (X-n)(n greate
r 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 Polis
h 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] Condit
ions on the distribution of l(F-n) are given for the existence of an i
nvariant distribution of X-0 making the process (X-n)(n greater than o
r equal to 0) stationary and ergodic. Our main result corrects a centr
al limit theorem by Loskot and Rudnicki [3] and removes an error in it
s 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 b
y a martingale difference scheme.