  In this paper, we define random quasi-periodic paths for random dynamical
systems and quasi-periodic measures for Markovian semigroups. We give a
sufficient condition for the existence and uniqueness of random quasi-periodic
paths and quasi-periodic measures for stochastic differential equations and a
sufficient condition for the density of the quasi-periodic measure to exist and
to satisfy the Fokker-Planck equation. We obtain an invariant measure by
considering lifted flow and semigroup on cylinder and the tightness of the
average of lifted quasi-periodic measures. We further prove that the invariant
measure is unique, and thus ergodic.
