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Scientific article
English

Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics

Contributors

Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.

Published in

SIAM journal on mathematical analysis, vol. 53, no. 1, p. 1-16

Publication date

2015

Abstract

A new characterization of sufficient conditions for the Lie-Trotter splitting to capture the numerical invariant measure of nonlinear ergodic Langevin dynamics up to an arbitrary order is discussed. Our characterization relies on backward error analysis and needs weaker assumptions than assumed so far in the literature. In particular, neither high weak order of the splitting scheme nor symplecticity are necessary to achieve high order approximation of the invariant measure of the Langevin dynamics. Numerical experiments confirm our theoretical findings.

Keywords

  • Stochastic differential equations
  • Splitting method
  • Langevin dynamics
  • Weak convergence
  • Modified differential equations
  • Backward error analysis
  • Invariant measure
  • Ergodicity

UNIGE affiliation entities

UNIGE research groups

Funding

  • Swiss National Science Foundation - 200020 144313/1

Citation (ISO format)

ABDULLE, Assyr, VILMART, Gilles, ZYGALAKIS, Konstantinos C. Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics. In: SIAM journal on mathematical analysis, 2015, vol. 53, n° 1, p. 1–16. doi: 10.1137/140962644

Main files (1)

Article (Submitted version)

Identifiers

Journal ISSN

0036-1410
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2downloads

Technical informations

Creation

12/11/2014 15:50:00

First validation

12/11/2014 15:50:00

Update

14/03/2023 22:15:21

Status update

14/03/2023 22:15:21

Last indexation

30/10/2024 20:45:19
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