Modulation Equations: Stochastic Bifurcation in Large Domains
  We consider the stochastic Swift-Hohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a stochastic Ginzburg-Landau equation. We then proceed to show that this approximation also extends to the invariant measures of these equations. 
D. Bl\"omker, M. Hairer, G. A. Pavliotis