# Analysis of Adaptive Multilevel Splitting algorithms in an idealized case

1 MATHERIALS - MATHematics for MatERIALS
ENPC - École des Ponts ParisTech, CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria Paris-Rocquencourt
Abstract : The Adaptive Multilevel Splitting algorithm is a very powerful and versatile method to estimate rare events probabilities. It is an iterative procedure on an interacting particle system, where at each step, the $k$ less well-adapted particles among $n$ are killed while $k$ new better adapted particles are resampled according to a conditional law. We analyze the algorithm in the idealized setting of an exact resampling and prove that the estimator of the rare event probability is unbiased whatever $k$. We also obtain a precise asymptotic expansion for the variance of the estimator and the cost of the algorithm in the large $n$ limit, for a fixed $k$.
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Cited literature [9 references]

https://hal.archives-ouvertes.fr/hal-00987297
Contributor : Charles-Edouard Bréhier <>
Submitted on : Tuesday, May 6, 2014 - 4:25:59 PM
Last modification on : Thursday, February 28, 2019 - 9:04:08 AM
Long-term archiving on : Wednesday, August 6, 2014 - 11:45:17 AM

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Charles-Edouard Bréhier, Tony Lelièvre, Mathias Rousset. Analysis of Adaptive Multilevel Splitting algorithms in an idealized case. ESAIM: Probability and Statistics, EDP Sciences, 2015, 19, ⟨10.1051/ps/2014029⟩. ⟨hal-00987297⟩

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