Journal of Statistical Physics

, Volume 164, Issue 4, pp 735–771 | Cite as

Error Analysis of Modified Langevin Dynamics

Article

Abstract

We consider Langevin dynamics associated with a modified kinetic energy vanishing for small momenta. This allows us to freeze slow particles, and hence avoid the re-computation of inter-particle forces, which leads to computational gains. On the other hand, the statistical error may increase since there are a priori more correlations in time. The aim of this work is first to prove the ergodicity of the modified Langevin dynamics (which fails to be hypoelliptic), and next to analyze how the asymptotic variance on ergodic averages depends on the parameters of the modified kinetic energy. Numerical results illustrate the approach, both for low-dimensional systems where we resort to a Galerkin approximation of the generator, and for more realistic systems using Monte Carlo simulations.

Keywords

Langevin dynamics Variance reduction Ergodicity Functional estimates Linear response 

Notes

Acknowledgments

Stephane Redon and Zofia Trstanova gratefully acknowledge funding from the European Research Council through the ERC Starting Grant No. 307629. This work was funded by the Agence Nationale de la Recherche, under Grant ANR-14-CE23-0012 (COSMOS). Gabriel Stoltz benefited from the scientific environment of the Laboratoire International Associé between the Centre National de la Recherche Scientifique and the University of Illinois at Urbana-Champaign.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Stephane Redon
    • 1
    • 2
  • Gabriel Stoltz
    • 3
  • Zofia Trstanova
    • 1
    • 2
  1. 1.INRIA Grenoble-Rhone-AlpesSaint Ismier CedexFrance
  2. 2.Laboratoire Jean KuntzmannGrenoble Cedex 9France
  3. 3.Université Paris-Est, CERMICS (ENPC), INRIAMarne-la-ValléeFrance

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