Scientific article

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

Published inSIAM journal on mathematical analysis, vol. 53, no. 1, p. 1-16
Publication date2015

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.

  • Stochastic differential equations
  • Splitting method
  • Langevin dynamics
  • Weak convergence
  • Modified differential equations
  • Backward error analysis
  • Invariant measure
  • Ergodicity
Research group
  • 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)
ISSN of the journal0036-1410

Technical informations

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