Invariant measures of dynamical systems generated e. g. by difference equations
can be computed by discretizing the originally continuum state space, and
replacing the action of the generator by the transition mechanism of a Markov
chain. In fact they are approximated by stationary vectors of these Markov
chains. Here we extend this well known approximation result and the underlying
algorithm to the setting of random dynamical systems, i.e. dynamical systems
on the skew product of a probability space carrying the underlying stationary
stochasticity and the state space, a particular non-autonomous framework. The
systems are generated by difference equations driven by stationary random processes
modelled on a metric dynamical system. The approximation algorithm
involves spatial discretizations and the definition of appropriate random Markov
chains with stationary vectors converging to the random invariant measure of
the system.