Optimal linear drift for the speed of convergence of an hypoelliptic diffusion

Arnaud Guillin (1) , Pierre Monmarché (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 Institut de Mathematiques Universite de Neuchatel

Among all generalized Ornstein-Uhlenbeck processes which sample the same invariant measure and for which the same amount of randomness (a $N$-dimensional Brownian motion) is injected in the system, we prove that the asymptotic rate of convergence is maximized by a non-reversible hypoelliptic one.

Mots clés: hypocoercivity; MCMC; Hypoelliptic diffusion

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Arnaud Guillin, Pierre Monmarché. Optimal linear drift for the speed of convergence of an hypoelliptic diffusion. 2016. ⟨hal-01306884v2⟩