Central Limit Theorem for Adaptative Multilevel Splitting Estimators in an Idealized Setting
Probability
2019-10-21 v1
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.
Cite
@article{arxiv.1501.01399,
title = {Central Limit Theorem for Adaptative Multilevel Splitting Estimators in an Idealized Setting},
author = {Charles-Edouard Bréhier and Ludovic Goudenège and Loic Tudela},
journal= {arXiv preprint arXiv:1501.01399},
year = {2019}
}