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December 2016 Unbiasedness of some generalized adaptive multilevel splitting algorithms
Charles-Edouard Bréhier, Maxime Gazeau, Ludovic Goudenège, Tony Lelièvre, Mathias Rousset
Ann. Appl. Probab. 26(6): 3559-3601 (December 2016). DOI: 10.1214/16-AAP1185


We introduce a generalization of the Adaptive Multilevel Splitting algorithm in the discrete time dynamic setting, namely when it is applied to sample rare events associated with paths of Markov chains. We build an estimator of the rare event probability (and of any nonnormalized quantity associated with this event) which is unbiased, whatever the choice of the importance function and the number of replicas. This has practical consequences on the use of this algorithm, which are illustrated through various numerical experiments.


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Charles-Edouard Bréhier. Maxime Gazeau. Ludovic Goudenège. Tony Lelièvre. Mathias Rousset. "Unbiasedness of some generalized adaptive multilevel splitting algorithms." Ann. Appl. Probab. 26 (6) 3559 - 3601, December 2016.


Received: 1 June 2015; Revised: 1 November 2015; Published: December 2016
First available in Project Euclid: 15 December 2016

zbMATH: 1361.65006
MathSciNet: MR3582811
Digital Object Identifier: 10.1214/16-AAP1185

Primary: 65C05 , 65C35

Keywords: adaptive multilevel splitting algorithms , Rare event , unbiased estimator

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.26 • No. 6 • December 2016
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