Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2001
 arXiv:
 arXiv:math/0109115
 Bibcode:
 2001math......9115H
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 60H15
 EPrint:
 41 pages