Annals of Applied Probability

Unbiasedness of some generalized adaptive multilevel splitting algorithms

Charles-Edouard Bréhier, Maxime Gazeau, Ludovic Goudenège, Tony Lelièvre, and Mathias Rousset

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 26, Number 6 (2016), 3559-3601.

Dates
Received: June 2015
Revised: November 2015
First available in Project Euclid: 15 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1481792593

Digital Object Identifier
doi:10.1214/16-AAP1185

Mathematical Reviews number (MathSciNet)
MR3582811

Zentralblatt MATH identifier
1361.65006

Subjects
Primary: 65C05: Monte Carlo methods 65C35: Stochastic particle methods [See also 82C80]

Keywords
Rare event adaptive multilevel splitting algorithms unbiased estimator

Citation

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


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