Optimal non-reversible linear drift for the convergence to equilibrium of a diffusion

Tony Lelièvre (1, 2) , Francis Nier (2, 3) , Grigorios A. Pavliotis (2, 4)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MICMAC - Methods and engineering of multiscale computing from atom to continuum
3 IRMAR - Institut de Recherche Mathématique de Rennes
4 Imperial College London

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.

Mots clés: Non-reversible diffusion; Convergence to equilibrium; Wick calculus

Domaines: Analyse numérique [math.NA]

Tony Lelièvre, Francis Nier, Grigorios A. Pavliotis. Optimal non-reversible linear drift for the convergence to equilibrium of a diffusion. Journal of Statistical Physics, 2013, 152 (2), pp.237-274. ⟨10.1007/s10955-013-0769-x⟩. ⟨hal-00761688⟩