Geometric ergodicity for stochastic pdes

This paper examines the geometric ergodicity of a semin-linear parabolic PDE forced by a Wiener process on a separable Hilbert space. Under a dissipative assumption on the vector field and a non-degeneracy assumption on the noise, geometric ergodicity is proved with respect to the class of measurable functions bounded by 1+‖·‖²The theorems apply under general conditions on the noise, both additive and multiplicative cases being considered, and apply for instance to a dissipative reaction-diffusion equation on [0,1] with a globally Lipschitz nonlinearity when forced by additive space-time white noise