Optimal linear drift for the speed of convergence of an hypoelliptic diffusion. (English) Zbl 1354.60084

Guillin, Arnaud; Monmarché, Pierre

Electron. Commun. Probab. 21, Paper No. 74, 14 p. (2016); erratum ibid. 22, Paper No. 15, 2 p. (2017).

Summary: 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.

MSC:

60J60	Diffusion processes
60F99	Limit theorems in probability theory
60J65	Brownian motion
35K10	Second-order parabolic equations
65C05	Monte Carlo methods

Keywords:

hypoelliptic diffusion; Ornstein-Uhlenbeck process; optimal linear dirft; hypocoercivity; Brownian motion; irreversibility; optimal sampling; asymptotic convergence rate