Central Limit Theorem for Adaptative Multilevel Splitting Estimators in an Idealized Setting

Abstract : The Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the authors prove that some associated estimators are unbiased, for each value of the size n of the systems of replicas and of resampling number k. Here we go beyond and prove these estimator's asymptotic normality when h goes to infinity, for any fixed value of k. The main ingredient is the asymptotic analysis of a functional equation on an appropriate characteristic function. Some numerical simulations illustrate the convergence to rely on Gaussian confidence intervals.
Document type :
Journal articles
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01074155
Contributor : Ludovic Goudenège <>
Submitted on : Monday, October 13, 2014 - 10:50:46 AM
Last modification on : Wednesday, September 12, 2018 - 2:24:10 PM
Long-term archiving on : Thursday, January 15, 2015 - 2:55:52 PM

Files

TCL_AMS-hal-arxiv.pdf
Files produced by the author(s)

Identifiers

Citation

Charles-Edouard Bréhier, Ludovic Goudenège, Loic Tudela. Central Limit Theorem for Adaptative Multilevel Splitting Estimators in an Idealized Setting. Springer Proceedings in Mathematics & Statistics, Springer, 2016, Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014, 163, pp.245--260. ⟨10.1007/978-3-319-33507-0_10⟩. ⟨hal-01074155⟩

Share

Metrics

Record views

387

Files downloads

142