The Adaptive Multilevel Splitting algorithm [F. Cérou and A. Guyader, Stoch. Anal. Appl. 25 (2007) 417–443] 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 less well-adapted particles among are killed while 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 . We also obtain a precise asymptotic expansion for the variance of the estimator and the cost of the algorithm in the large limit, for a fixed .
DOI : 10.1051/ps/2014029
Mots-clés : Monte-Carlo simulation, rare events, multilevel splitting
@article{PS_2015__19__361_0,
author = {Br\'ehier, Charles-Edouard and Leli\`evre, Tony and Rousset, Mathias},
title = {Analysis of adaptive multilevel splitting algorithms in an idealized case},
journal = {ESAIM: Probability and Statistics},
pages = {361--394},
publisher = {EDP-Sciences},
volume = {19},
year = {2015},
doi = {10.1051/ps/2014029},
zbl = {1348.65017},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2014029/}
}
TY - JOUR AU - Bréhier, Charles-Edouard AU - Lelièvre, Tony AU - Rousset, Mathias TI - Analysis of adaptive multilevel splitting algorithms in an idealized case JO - ESAIM: Probability and Statistics PY - 2015 SP - 361 EP - 394 VL - 19 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2014029/ DO - 10.1051/ps/2014029 LA - en ID - PS_2015__19__361_0 ER -
%0 Journal Article %A Bréhier, Charles-Edouard %A Lelièvre, Tony %A Rousset, Mathias %T Analysis of adaptive multilevel splitting algorithms in an idealized case %J ESAIM: Probability and Statistics %D 2015 %P 361-394 %V 19 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2014029/ %R 10.1051/ps/2014029 %G en %F PS_2015__19__361_0
Bréhier, Charles-Edouard; Lelièvre, Tony; Rousset, Mathias. Analysis of adaptive multilevel splitting algorithms in an idealized case. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 361-394. doi : 10.1051/ps/2014029. http://archive.numdam.org/articles/10.1051/ps/2014029/
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