  The paper is devoted to constructing a random exponential attractor for some
classes of stochastic PDE's. We first prove the existence of an exponential
attractor for abstract random dynamical systems and study its dependence on a
parameter and then apply these results to a nonlinear reaction-diffusion system
with a random perturbation. We show, in particular, that the attractors can be
constructed in such a way that the symmetric distance between the attractors
for stochastic and deterministic problems goes to zero with the amplitude of
the random perturbation.
