On a class of stable random dynamical systems: Theory and applications

We consider a random dynamical system in which the state space is an interv al. and possible laws of motion are monotone functions. It is shown that if the Markov process generated by this system satisfies a splitting conditio n, it converges to a unique invariant distribution exponentially fast in th e Kolmogorov distance. A central limit theorem on the lime-averages of obse rved values of the states is also proved. As an application we consider a s ystem that captures an interaction of growth and cyclical forces: of two po ssible laws, on is monotone, but the other is unimodal with two periodic po ints. Journal of Economic Literature Classification Numbers: C6, D9. (C) 20 01 Academic Press.