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arXiv:math/0109115math.PR

Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling

Martin Hairer

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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.

arXiv comments
41 pages
Journal reference
DOI
Subjects
math.PRProbability math-phMathematical Physics

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  1. "the very foundation of modern academia has been blown to bits" 1 comment

    • Man, I had forgotten about this one. Thanks for the highlight, I read Okazaki's the first time about 2014/15 IIRC. Another great read is "A Theory of Regularity Structures" - https://arxiv.org/pdf/1303.5113. by Martin Hairer. It builds on his thesis, Comportement Asymptotique d’…

      naishoyaView on HNParent context

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