ABSTRACT
In the present chapter the results obtained before are going to be applied to random dynamical systems (RDS). We will give only the abstract characterisation of RDS. For a comprehensive and thorough description of the generation of RDS from random and stochastic differential equations in finite dimensional spaces we refer to Arnold [I], in particular to Chapter 2. Concerning the generation of RDS from infinite-dimensional problems, in particular from stochastic parabolic stochastic partial differential equations on bounded domains, ser Flandoli [23]. The results we are interested here are assertions about existence of invariant measures and of invariant lLIarkov measures for RDS on Polish spaces, as well as a cllaracterisation of the convergence of time means in terms of integrals over ergodic invariant measures. These results are the ones which need the topological prerequisites obtained in previous chapters.
