  We explore Ito stochastic differential equations where the drift term
possibly depends on the infinite past. Assuming the existence of a Lyapunov
function, we prove the existence of a stationary solution assuming only minimal
continuity of the coefficients. Uniqueness of the stationary solution is proven
if the dependence on the past decays sufficiently fast. The results of this
paper are then applied to stochastically forced dissipative partial
differential equations such as the stochastic Navier-Stokes equation and
stochastic Ginsburg-Landau equation.
