Imperial College London
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Professor Grigorios A. Pavliotis

Faculty of Natural Sciences, Department of Mathematics

Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8564g.pavliotis Website

 
 
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Location

 

736aHuxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Abdulle:2019:10.1016/j.crma.2019.04.008,
author = {Abdulle, A and Pavliotis, GA and Vilmart, G},
doi = {10.1016/j.crma.2019.04.008},
journal = {Comptes Rendus Mathematique (Academie des Sciences)},
pages = {349--354},
title = {Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations},
url = {http://dx.doi.org/10.1016/j.crma.2019.04.008},
volume = {357},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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 et al. (1993)[1]and studied in, e.g., T. Lelièvre et al. (2013)[2]and A.B. Duncan et al. (2016)[3], 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.
AU  - Abdulle,A
AU  - Pavliotis,GA
AU  - Vilmart,G
DO  - 10.1016/j.crma.2019.04.008
EP  - 354
PY  - 2019///
SN  - 0764-4442
SP  - 349
TI  - Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations
T2  - Comptes Rendus Mathematique (Academie des Sciences)
UR  - http://dx.doi.org/10.1016/j.crma.2019.04.008
UR  - http://hdl.handle.net/10044/1/76562
VL  - 357
ER  -
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