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Invariant Measures for Stochastic PDE's in Unbounded Domains

J. -P. Eckmann·M. Hairer
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Abstract

We study stochastically forced semilinear parabolic PDE's of the Ginzburg-Landau type. The class of forcings considered are white noises in time and colored smooth noises in space. Existence of the dynamics in $L^\infty$, as well as existence of an invariant measure are proven. We also show that the solutions are with high probability analytic in a strip around the real axis and give estimates on the width of that strip.

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J. -P. Eckmann, M. Hairer. 2000-03-28. Invariant Measures for Stochastic PDE's in Unbounded Domains. https://doi.org/10.1088/0951-7715%2F14%2F1%2F308

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