Invariant measure for the stochastic Ginzburg Landau equation

The existence of martingale solutions and stationary solutions of stochastic Ginzburg-Landau equations under general hypothesizes on the dimension, the non linearterm and the added noise is investigated. With a few more assumptions, it is establishedthat the transition semi-group is well defined and that the stationary martingalesolution yields the existence of an invariant measure. Moreover this invariant measure is shown to be unique.