Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 26, Number 6 (2016), 3559-3601.
Unbiasedness of some generalized adaptive multilevel splitting algorithms
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.
Ann. Appl. Probab., Volume 26, Number 6 (2016), 3559-3601.
Received: June 2015
Revised: November 2015
First available in Project Euclid: 15 December 2016
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Bréhier, Charles-Edouard; Gazeau, Maxime; Goudenège, Ludovic; Lelièvre, Tony; Rousset, Mathias. Unbiasedness of some generalized adaptive multilevel splitting algorithms. Ann. Appl. Probab. 26 (2016), no. 6, 3559--3601. doi:10.1214/16-AAP1185. https://projecteuclid.org/euclid.aoap/1481792593