Invariant Measures for Stochastic PDE's in Unbounded Domains
  We study stochastically forced semilinear parabolic PDE's of the Ginzburg-Landau type. The class of forcings considered are white noises in time and colored smooth noises in space. Existence of the dynamics in $L^\infty$, as well as existence of an invariant measure are proven. We also show that the solutions are with high probability analytic in a strip around the real axis and give estimates on the width of that strip. 
J.-P. Eckmann, M. Hairer