  In this paper we propose a new approach for sampling from probability
measures in, possibly, high dimensional spaces. By perturbing the standard
overdamped Langevin dynamics by a suitable Stratonovich perturbation that
preserves the invariant measure of the original system, we show that
accelerated convergence to equilibrium and reduced asymptotic variance can be
achieved, leading, thus, to a computationally advantageous sampling algorithm.
The new perturbed Langevin dynamics is reversible with respect to the target
probability measure and, consequently, does not suffer from the drawbacks of
the nonreversible Langevin samplers that were introduced in~[C.-R. Hwang, S.-Y.
Hwang-Ma, and S.-J. Sheu, Ann. Appl. Probab. 1993] and studied in, e.g. [T.
Lelievre, F. Nier, and G. A. Pavliotis J. Stat. Phys., 2013] and [A. B. Duncan,
T. Leli\`evre, and G. A. Pavliotis J. Stat. Phys., 2016], while retaining all
of their advantages in terms of accelerated convergence and reduced asymptotic
variance. In particular, the reversibility of the dynamics ensures that there
is no oscillatory transient behaviour. The improved performance of the proposed
methodology, in comparison to the standard overdamped Langevin dynamics and its
nonreversible perturbation, is illustrated on an example of sampling from a
two-dimensional warped Gaussian target distribution.
