Pathwise Estimates for Effective Dynamics: The Case of Nonlinear Vectorial Reaction Coordinates

Tony Lelièvre (1, 2) , Wei Zhang (3)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MATHERIALS - MATHematics for MatERIALS
3 ZIB - Zuse Institute Berlin

Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Lelièvre, Nonlinearity, 23 (2010), pp. 2131--2163] to approximate the essential dynamics of high-dimensional diffusion processes along a given reaction coordinate. The approximation error of the effective dynamics when it is used to approximate the behavior of the original dynamics has been considered in recent years. As a continuation of the previous work [F. Legoll, T. Lelièvre, and S. Olla, Stochastic Process. Appl., 127 (2017), pp. 2841--2863], in this paper we obtain pathwise estimates of effective dynamics for both nonlinear and vector-valued reaction coordinate functions.

Mots clés: Diffusion process; Effective dynamics; Reaction coordinate; Time scale separation; Pathwise estimates

Domaines: Analyse numérique [math.NA]

Tony Lelièvre, Wei Zhang. Pathwise Estimates for Effective Dynamics: The Case of Nonlinear Vectorial Reaction Coordinates. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2019, 17 (3), pp.1019-1051. ⟨10.1137/18M1186034⟩. ⟨hal-02383239⟩