Attractors for random dynamical systems (Q1343608)

Random dynamical systems are treated, the notions of an omega limit set, a random invariant set, an absorbing set and a global attractor are introduced. Conditions are given under which a global attractor (being a compact random invariant set) exists, and some of its properties are established. The theory is then applied to a reaction-diffusion equation with additive noise and to the stochastic Navier-Stokes equation with multiplicative, resp. additive noise. In all the three cases the existence of a compact stochastic attractor is proved.