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  1. Martin Hairer Mathematics Department, Imperial College London Email: m.hairer@imperial.ac.uk Abstract The aim of this minicourse is to provide a number of tools that allow one to de-termine at which speed (if at all) the law of a diffusion process, or indeed a rather general Markov process, approaches its stationary distribution. Of particular in-

  2. 3.4 The Cameron-Martin space 23 3.5 Images of Gaussian measures 28 3.6 Disintegration of Gaussian measures 32 3.7 Cylindrical Wiener processes and stochastic integration 34 4 Elements of Semigroup Theory 39 4.1 Strongly continuous semigroups 41 4.2 Semigroups with selfadjoint generators 45 4.3 Analytic semigroups 46 4.4 Interpolation spaces 49

  3. Few mathematicians work in isolation and I’ve been fortunate to be able to interact with many colleagues and collaborators, learning much in the process. The work recognized by this prize could not have existed without the contributions of many others. I would also like to thank the Leverhulme Trust, the ERC, and the Royal Society whose ...

  4. Martin Hairer vom Imperial College London wurde für seine Theorien zur Lösung von Gleichungen, die Zufallsprozesse beschreiben, mit dem Breakthrough-Prize geehrt. Foto: APA/HANS PUNZ Wien/San Francisco – Der österreichische Mathematiker Martin Hairer (44) vom Imperial College London wird mit dem Breakthrough-Preis 2021 in Mathematik ausgezeichnet.

  5. Martin Hutzenthaler University of Duisburg-Essen, ... A Apte, M Hairer, AM Stuart, J Voss. Physica D: Nonlinear Phenomena 230 (1-2), 50-64, 2007. 143: 2007: Ergodicity of stochastic differential equations driven by fractional Brownian motion . M Hairer. ...

  6. Written in collaboration with D. Blömker . Commun. Math. Phys. 251 (2004), no 3, pp. 515-555 Published version. PDF File. Ergodicity of the 2D Navier-Stokes Equations with Degenerate Stochastic Forcing. Written in collaboration with J. Mattingly . Annals of Maths 164 (2006), no 3, pp. 993-1032 Published version. PDF File.

  7. [4]M. Hairer, Exponential Mixing for a Stochastic PDE Driven by Degenerate Noise, Nonlinearity 15 (2002), pp. 271–279 [5]M. Hairer, Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling, Probab. Theory Relat. Fields 124 (2002), no 3, pp. 345–380