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The Adaptive Multilevel Splitting (AMS) algorithm is a powerful and versatilemethod for the simulation of rare events. It is based on an interacting (via amutation-selection procedure) system of replicas, and depends on two integerparameters: n $\in$ N * the size of the system and the number k $\in$ {1, . . ., n -- 1} of the replicas that are eliminated and resampled at each iteration.In an idealized setting, we analyze the performance of this algorithm in termsof a Large Deviations Principle when n goes to infinity, for the estimation ofthe (small) probability P(X \textgreater{} a) where a is a given threshold andX is real-valued random variable. The proof uses the technique introduced in[BLR15]: in order to study the log-Laplace transform, we rely on an auxiliaryfunctional equation. Such Large Deviations Principle results are potentiallyuseful to study the algorithm beyond the idealized setting, in particular tocompute rare transitions probabilities for complex high-dimensional stochasticprocesses.

Large deviations principle for the Adaptive Multilevel Splitting Algorithm in an idealized setting