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

Charles-Edouard Bréhier (1, 2) , Ludovic Goudenège (3) , Loic Tudela (4)

1 MATHERIALS - MATHematics for MatERIALS
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 FR3487 - Fédération de Mathématiques de l'Ecole Centrale Paris
4 ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique

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.

Mots clés: Stochastic particle methods; Monte Carlo methods; Central Limit Theorem

Domaines: Probabilités [math.PR]

Charles-Edouard Bréhier, Ludovic Goudenège, Loic Tudela. Central Limit Theorem for Adaptative Multilevel Splitting Estimators in an Idealized Setting. Springer Proceedings in Mathematics & Statistics, 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⟩