Journal of Statistical Physics

, Volume 152, Issue 2, pp 237–274 | Cite as

Optimal Non-reversible Linear Drift for the Convergence to Equilibrium of a Diffusion



We consider non-reversible perturbations of reversible diffusions that do not alter the invariant distribution and we ask whether there exists an optimal perturbation such that the rate of convergence to equilibrium is maximized. We solve this problem for the case of linear drift by proving the existence of such optimal perturbations and by providing an easily implementable algorithm for constructing them. We discuss in particular the role of the prefactor in the exponential convergence estimate. Our rigorous results are illustrated by numerical experiments.


Non-reversible diffusion Convergence to equilibrium Wick calculus 



We would like to thank Matthieu Dubois for preliminary numerical experiments.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.CERMICS, Ecole des pontsUniversité Paris-EstMarne la Vallée cedex 2France
  2. 2.MicMac project teamINRIALe Chesnay cedexFrance
  3. 3.IRMAR, Campus de BeaulieuUniversité de Rennes 1RennesFrance
  4. 4.Department of MathematicsImperial College LondonLondonEngland

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