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In this paper we propose a new approach for sampling from probabilitymeasures in, possibly, high dimensional spaces. By perturbing the standardoverdamped Langevin dynamics by a suitable Stratonovich perturbation thatpreserves the invariant measure of the original system, we show thataccelerated convergence to equilibrium and reduced asymptotic variance can beachieved, leading, thus, to a computationally advantageous sampling algorithm.The new perturbed Langevin dynamics is reversible with respect to the targetprobability measure and, consequently, does not suffer from the drawbacks ofthe 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 allof their advantages in terms of accelerated convergence and reduced asymptoticvariance. In particular, the reversibility of the dynamics ensures that thereis no oscillatory transient behaviour. The improved performance of the proposedmethodology, in comparison to the standard overdamped Langevin dynamics and itsnonreversible perturbation, is illustrated on an example of sampling from atwo-dimensional warped Gaussian target distribution.

Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations