  We study the problem of exponential mixing and large deviations for
discrete-time Markov processes associated with a class of random dynamical
systems. Under some dissipativity and regularisation hypotheses for the
underlying deterministic dynamics and a non-degeneracy condition for the
driving random force, we discuss the existence and uniqueness of a stationary
measure and its exponential stability in the Kantorovich-Wasserstein metric. We
next turn to the large deviation principle and establish its validity for the
occupation measures of the Markov processes in question. The obtained results
extend those established earlier for the case of the bounded noise and can be
applied to the 2D Navier-Stokes system in a bounded domain and to the complex
Ginzburg-Landau equation.
