Under a dissipativity condition, a stochastic differential equation with quasi-periodic coefficients has a unique random quasi-periodic path, a unique quasi-periodic measure, and a unique ergodic invariant measure on a lifted cylinder.
Arnold, Random Dynamical Systems , Springer-Verlag Berlin Heidelberg New York, 1998
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Random quasi-periodic paths and quasi-periodic measures of stochastic differential equations
Under a dissipativity condition, a stochastic differential equation with quasi-periodic coefficients has a unique random quasi-periodic path, a unique quasi-periodic measure, and a unique ergodic invariant measure on a lifted cylinder.