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Ergodicity for a class of Markov processes and applications to randomly forced PDE’s. II. (English) Zbl 1132.60319

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 S. Kuksin [J. Phys. A, Math. Gen. 37, No. 12, 3805–3822 (2004; Zbl 1047.35061)].

MSC:

60J25 Continuous-time Markov processes on general state spaces
35R60 PDEs with randomness, stochastic partial differential equations
35K55 Nonlinear parabolic equations
37L55 Infinite-dimensional random dynamical systems; stochastic equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35Q60 PDEs in connection with optics and electromagnetic theory
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