I consider discretized random perturbations
of hyperbolic dynamical systems
and prove that when perturbation
parameter tends to zero invariant measures
of corresponding Markov chains converge to
the Sinai-Bowen-Ruelle measure of the dynamical system. This
provides a robust method for computations of
such measures and for visualizations of some hyperbolic
attractors by modeling randomly perturbed
dynamical systems on a computer.
Similar results are true for
discretized random perturbations
of maps of the interval satisfying the Misiurewicz
condition considered in [KK].