Communications in Mathematical Physics

, Volume 251, Issue 3, pp 515–555 | Cite as

Multiscale Expansion of Invariant Measures for SPDEs

  • Dirk Blömker
  • Martin Hairer


We derive the first two terms in an ɛ-expansion for the invariant measure of a class of semilinear parabolic SPDEs near a change of stability, when the noise strength and the linear instability are of comparable order ɛ2. This result gives insight into the stochastic bifurcation and allows to rigorously approximate correlation functions. The error between the approximate and the true invariant measure is bounded in both the Wasserstein and the total variation distance.


Neural Network Statistical Physic Correlation Function Complex System Total Variation 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Mathematics Research CentreUniversity of WarwickCoventryUnited Kingdom
  2. 2.Institut für Mathematik, RWTH Aachen AachenGermany

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