Communications in Mathematical Physics

, Volume 258, Issue 2, pp 479–512 | Cite as

Modulation Equations: Stochastic Bifurcation in Large Domains

  • D. Blömker
  • M. Hairer
  • G. A. Pavliotis


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.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Invariant Measure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Institut für Mathematik, RWTH AachenAachenGermany
  2. 2.Dept. of MathematicsThe University of Warwick 
  3. 3.Dept. of MathematicsImperial CollegeLondon

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