Integrable Systems, Analysis And Probability Seminar
Thursday, December 4, 2003, 4:00pm, 120 Physics
Martin Hairer (University of Warwick)
Stochastic amplitude equations
Abstract:- The dynamic of PDEs near a (deterministic) bifurcation point can be
well understood in terms of an associated finite-dimensional amplitude equation. We show that in the stochastic case, this is still true, but
that the analysis can be carried on further to give information about the invariant measure of the stochastic PDE. The invariant measure
of the associated amplitude equation can indeed be interpreted as the
first term in a multiscale expansion for the invariant measure of the
full equation. The second term in this expansion turns out to be a
Gaussian measure which can also be characterized explicitely.
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