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Journal Articles Chaos: An Interdisciplinary Journal of Nonlinear Science Year : 2019

Adaptive Multilevel Splitting: Historical Perspective and Recent Results

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Abstract

This article first presents a short historical perpective of the importance splitting approach to simulate and estimate rare events, with a detailed description of several variants. We then give an account of recent theoretical results on these algorithms, including a central limit theorem for Adaptive Multilevel Splitting (AMS). Considering the asymptotic variance in the latter, the choice of the importance function, called the reaction coordinate in molecular dynamics, is also discussed. Finally, we briefly mention some worthwhile applications of AMS in various domains.
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Dates and versions

hal-01936611 , version 1 (27-11-2018)
hal-01936611 , version 2 (24-04-2019)

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Frédéric Cérou, Arnaud Guyader, Mathias Rousset. Adaptive Multilevel Splitting: Historical Perspective and Recent Results. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019, 29 (4), pp.1-32. ⟨10.1063/1.5082247⟩. ⟨hal-01936611v2⟩
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