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Journal Articles SIAM/ASA Journal on Uncertainty Quantification Year : 2019

On the Asymptotic Normality of Adaptive Multilevel Splitting

Abstract

Adaptive Multilevel Splitting (AMS for short) is a generic Monte Carlo method for Markov processes that simulates rare events and estimates associated probabilities. Despite its practical efficiency, there are almost no theoretical results on the convergence of this algorithm. The purpose of this paper is to prove both consistency and asymptotic normality results in a general setting. This is done by associating to the original Markov process a level-indexed process, also called a stochastic wave, and by showing that AMS can then be seen as a Fleming-Viot type particle system. This being done, we can finally apply general results on Fleming-Viot particle systems that we have recently obtained.

Dates and versions

hal-01774856 , version 1 (24-04-2018)

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Frédéric Cérou, Bernard Delyon, Arnaud Guyader, Mathias Rousset. On the Asymptotic Normality of Adaptive Multilevel Splitting. SIAM/ASA Journal on Uncertainty Quantification, 2019, 7 (1), pp.1-30. ⟨10.1137/18M1187477⟩. ⟨hal-01774856⟩
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