The Adaptive Multilevel Splitting (AMS) algorithm is a powerful and versatile iterative method to estimate the probabilities of rare events. We prove a new central limit theorem for the associated AMS estimators introduced in [5], and which have been recently revisited in [3]-the main result there being (nonasymptotic) unbiasedness of the estimators. To prove asymptotic normality, we rely on and extend the technique presented in [3]: the (asymptotic) analysis of an integral equation. Numerical simulations illustrate the convergence and the construction of Gaussian confidence intervals.
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