Existence, uniqueness and convergence of a particle approximation for the Adaptive Biasing Force process

Benjamin Jourdain (1) , Tony Lelièvre (1) , Raphaël Roux (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

We prove existence and uniqueness for some nonlinear stochastic differential equation used in molecular dynamics, whose nonlinearity comes from a conditional expectation term. We also introduce an interacting particle system in order to approximate this conditional expectation, providing a discretization scheme for this equation.

Mots clés: free energy calculations; nonlinear stochastic differential equation; Fokker-Planck equation; interacting particle system; conditional expectation; Nadaraya-Watson estimator

Domaines: Probabilités [math.PR]

Benjamin Jourdain, Tony Lelièvre, Raphaël Roux. Existence, uniqueness and convergence of a particle approximation for the Adaptive Biasing Force process. ESAIM: Mathematical Modelling and Numerical Analysis, 2010, 44 (05), pp.831-865. ⟨10.1051/m2an/2010044⟩. ⟨hal-00370821v2⟩