Existence, uniqueness and convergence of a particle approximation for the adaptive biasing force process

ESAIM: Mathematical Modelling and Numerical Analysis

Volumn 44, Issue 5, 2010, Pages 831-865

  Jourdain, Benjamin ^a   Lelièvre, Tony ^a   Roux, Raphaël ^a  

^a UNIVERSITÉ PARIS EST   (France)

Author keywords

Adaptive biasing force method; Conditional McKean nonlinearity; Interacting particle systems

Indexed keywords

EID: 77956766161     PISSN: 28227840     EISSN: 28047214     Source Type: Journal    
DOI: 10.1051/m2an/2010044     Document Type: Article

References (19)

1. R. Adams, Sobolev spaces. Academic Press (1978).
2. M. Bossy, J.F. Jabir and D. Talay, On conditional McKean Lagrangian stochastic models. Prob. Theor. Relat. Fields (to appear).
3. H. Brézis, Analyse fonctionnelle. Théorie et applications. Collection Mathématiques appliquées pour la mâitrise, Masson, Paris (1983).
4. C. Chipot and A. Pohorille Eds., Free Energy Calculations, Springer Series in Chemical Physics 86. Springer (2007).
5. E. Darve and A. Pohorille, Calculating free energy using average forces. J. Chem. Phys. 115 (2001) 9169-9183.
6. R. Dautray and P.L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology. Springer Verlag (1999).
7. A. Dermoune, Propagation and conditional propagation of chaos for pressureless gas equations. Prob. Theor. Relat. Fields 126 (2003) 459-479.
8. J. Hénin and C. Chipot, Overcoming free energy barriers using unconstrained molecular dynamics simulations. J. Chem. Phys. 121 (2004) 2904-2914.
9. N.V. Krylov and M. Röckner, Strong solutions of stochastic equations with singular time dependent drift. Prob. Theor. Relat. Fields 131 (2005) 154-196.
10. T. Lelièvre, M. Rousset and G. Stoltz, Computation of free energy profiles with parallel adaptive dynamics. J. Chem. Phys. 126 (2007) 134111.
11. T. Lelièvre, M. Rousset and G. Stoltz, Long-time convergence of an adaptive biasing force method. Nonlinearity 21 (2008) 1155-1181.
12. J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non-linéaires. Dunod (1969).
13. J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Dunod, Paris (1968-1970).
14. P. Metzner, C. Schütte and E. Vanden-Eijnden, Illustration of transition path theory on a collection of simple examples. J. Chem. Phys. 125 (2006) 084110.
15. A.S. Sznitman, Topics in propagation of chaos, Lecture notes in mathematics 1464. Springer-Verlag (1989).
16. D. Talay and O. Vaillant, A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations. Ann. Appl. Prob. 13 (2003) 140-180.
17. R. Temam, Navier-Stokes equations and nonlinear functionnal analysis. North Holland, Amsterdam (1979).
18. V.C. Tran, A wavelet particle approximation for McKean-Vlasov and 2D-Navier-Stokes statistical solutions. Stoch. Proc. Appl. 118 (2008) 284-318.
19. A.B. Tsybakov, Introduction à l'estimation non- paramétrique. Springer (2004).