Analysis of Adaptive Multilevel Splitting algorithms in an idealized case

Charles-Edouard Bréhier (1, 2) , Tony Lelièvre (1, 2) , Mathias Rousset (1, 2)

1 MATHERIALS - MATHematics for MatERIALS
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

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 $k$.

Mots clés: rare events; Monte-Carlo simulation; multilevel splitting

Domaines: Probabilités [math.PR]

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