Modulation equations: Stochastic bifurcation in large domains - Blomker,D; Hairer,M; Pavliotis,GA (COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2005)
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.