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 non linear stochastic differential equation used in molecular dynamics, whose non linearity 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. 2009. ⟨hal-00370821v1⟩