Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling

Details Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling

2001-09-18

arxiv.org/abs/math/0109115v1

Mathematics

Probability

41 pages

Scientific paper

We consider parabolic stochastic partial differential equations driven by white noise in time. We prove exponential convergence of the transition probabilities towards a unique invariant measure under suitable conditions. These conditions amount essentially to the fact that the equation transmits the noise to all its determining modes. Several examples are investigated, including some where the noise does not act on every determining mode directly.

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