## Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling (2001)

Venue: | Probab. Theory Related Fields |

Citations: | 26 - 7 self |

### BibTeX

@ARTICLE{Hairer01exponentialmixing,

author = {M. Hairer},

title = {Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling},

journal = {Probab. Theory Related Fields},

year = {2001},

volume = {124},

pages = {200--2}

}

### Years of Citing Articles

### OpenURL

### 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.

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Citation Context ...e range of Q in H is "small". The investigation of asymptotic behaviour for solutions of (1.1) goes back to the early eighties (see for example [MS99] for an excellent review article or the =-=monograph [DPZ96] for a det-=-ailed exposition). Until recently, two approaches dominated the literature on this subject. For the first approach, sometimes called the "dissipativity method", one considers two solutions x... |

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Citation Context ...very determining mode of the equation. In this paper, we extend the coupling method to problems which do not satisfy this condition. Our overall approach is similar to the one exposed by Mattingly in =-=[Mat01]-=-, and consequently some of our proofs are closely related to the arguments exposed there. Our main new idea is to INTRODUCTION 4 construct a coupling for which the low-frequency parts of the dynamics ... |

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Citation Context ...sense), although the noise is weak, in the sense that the range of Q in H is "small". The investigation of asymptotic behaviour for solutions of (1.1) goes back to the early eighties (see fo=-=r example [MS99]-=- for an excellent review article or the monograph [DPZ96] for a detailed exposition). Until recently, two approaches dominated the literature on this subject. For the first approach, sometimes called ... |

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