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Exponential mixing properties of stochastic PDEs through asymptotic coupling
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  • Published: November 2002

Exponential mixing properties of stochastic PDEs through asymptotic coupling

  • M. Hairer1 

Probability Theory and Related Fields volume 124, pages 345–380 (2002)Cite this article

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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.

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Authors and Affiliations

  1. Département de Physique Théorique, Université de Genève, 1211 Genève 4, Switzerland. e-mail: Martin.Hairer@physics.unige.ch, , , , , , CH

    M. Hairer

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  1. M. Hairer
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Received: 20 September 2001 / Revised version: 21 April 2002 / Published online: 10 September 2002

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Hairer, M. Exponential mixing properties of stochastic PDEs through asymptotic coupling. Probab Theory Relat Fields 124, 345–380 (2002). https://doi.org/10.1007/s004400200216

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  • Issue Date: November 2002

  • DOI: https://doi.org/10.1007/s004400200216

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • White Noise
  • Invariant Measure
  • Suitable Condition
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