# Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates

2 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris
Abstract : Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Leli\evre, Nonlinearity, 2010] 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. Leli\evre, and S. Olla, Stoch. Process. Appl, 2017], in this paper we obtain pathwise estimates for effective dynamics when the reaction coordinate function is either nonlinear or vector-valued.
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https://hal.archives-ouvertes.fr/hal-01794919
Contributor : Tony Lelièvre <>
Submitted on : Friday, May 18, 2018 - 7:31:37 AM
Last modification on : Friday, April 19, 2019 - 4:55:26 PM

### Identifiers

• HAL Id : hal-01794919, version 1
• ARXIV : 1805.01928

### Citation

Tony Lelièvre, Wei Zhang. Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates. 2018. ⟨hal-01794919⟩

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