Uniqueness of the Invariant Measure¶for a Stochastic PDE Driven by Degenerate Noise

@article{Eckmann2001UniquenessOT,
  title={Uniqueness of the Invariant Measure¶for a Stochastic PDE Driven by Degenerate Noise},
  author={Jean-Pierre Eckmann and Martin Hairer},
  journal={Communications in Mathematical Physics},
  year={2001},
  volume={219},
  pages={523-565}
}
Abstract: We consider the stochastic Ginzburg–Landau equation in a bounded domain. We assume the stochastic forcing acts only on high spatial frequencies. The low-lying frequencies are then only connected to this forcing through the non-linear (cubic) term of the Ginzburg–Landau equation. Under these assumptions, we show that the stochastic PDE has a unique invariant measure. The techniques of proof combine a controllability argument for thelow-lying frequencies with an infinite dimensional… CONTINUE READING
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