Address. Mathematical Institute, Academy of Sciences, Zitna 25, 115 67 Praha 1, Czech Republic
Abstract. The paper presents a review of some recent results on uniqueness of invariant measures for stochastic differential equations in infinite-dimensional state spaces, with particular attention paid to stochastic partial differential equations. Related results on asymptotic behaviour of solutions like ergodic theorems and convergence of probability laws of solutions in strong and weak topologies are also reviewed.
AMS classification. 60H15
Key words. Stochastic evolution equations, invariant measures, ergodic theorems, stability