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Random Attractors for Stochastic Partly Dissipative Systems

We prove the existence of a global random attractor for a certain class of stochastic partly dissipative systems. These systems consist of a partial (PDE) and an ordinary differential equation (ODE), where both equations are coupled and perturbed by additive white noise. The deterministic counterpart of such systems and their long-time behaviour have already been considered but there is no theory that deals with the stochastic version of partly dissipative systems in their full generality. We also provide several examples for the application of the theory.