  We study a stochastic complex Ginzburg--Landau (CGL) equation driven by a
smooth noise in space and we establish exponential convergence of the Markovian
transition semi-group toward a unique invariant probability measure. Since Doob
Theorem does not seem not to be useful in our situation, a coupling method is
used. In order to make this method easier to understand, we first focus on two
simple examples which contain most of the arguments and the essential
difficulties.
