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

Tony Lelièvre; Wei Zhang

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arXiv · 1805.01928

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

Tony Lelièvre·Wei Zhang

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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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Tony Lelièvre, Wei Zhang. 2018-05-04. Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates. https://arxiv.org/abs/1805.01928

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