Ergodicity for a class of Markov processes and applications to randomly forced PDE's. II (Q2471405)

The paper is devoted to studying the problem of ergodicity for the complex Landau-Ginzburg (CGL) equation perturbed by an external random force. We show that the conditions of a simple general result established in the first part [Russ. J. Math. Phys. 12, No. 1, 81--96 (2005; Zbl 1132.60317)] are fulfilled for the equation in question. As a consequence, we prove that the corresponding family of Markov processes has a unique stationary distribution, which possesses a mixing property. The result of this paper was announced in a joint work with \textit{S. Kuksin} [J. Phys. A, Math. Gen. 37, No. 12, 3805--3822 (2004; Zbl 1047.35061)].