  We consider the stochastic CGL equation $$ \dot u- \nu\Delta u+(i+a) |u|^2u
=\eta(t,x),\;\;\; \text {dim} \,x=n, $$ where $\nu>0$ and $a\ge 0$, in a cube
(or in a smooth bounded domain) with Dirichlet boundary condition. The force
$\eta$ is white in time, regular in $x$ and non-degenerate. We study this
equation in the space of continuous complex functions $u(x)$, and prove that
for any $n$ it defines there a unique mixing Markov process. So for a large
class of functionals $f(u(\cdot))$ and for any solution $u(t,x)$, the averaged
observable $\E f(u(t,\cdot))$ converges to a quantity, independent from the
initial data $u(0,x)$, and equal to the integral of $f(u)$ against the unique
stationary measure of the equation.
