The Annals of Applied Probability

Fluctuation analysis of adaptive multilevel splitting

Frédéric Cérou and Arnaud Guyader

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Abstract

Multilevel Splitting, also called Subset Simulation, is a Sequential Monte Carlo method to simulate realisations of a rare event as well as to estimate its probability. This article is concerned with the convergence and the fluctuation analysis of Adaptive Multilevel Splitting techniques. In contrast to their fixed level version, adaptive techniques estimate the sequence of levels on the fly and in an optimal way, with only a low additional computational cost. However, very few convergence results are available for this class of adaptive branching models, mainly because the sequence of levels depends on the occupation measures of the particle systems. This article proves the consistency of these methods as well as a central limit theorem. In particular, we show that the precision of the adaptive version is the same as the one of the fixed-levels version where the levels would have been placed in an optimal manner.

Article information

Source
Ann. Appl. Probab., Volume 26, Number 6 (2016), 3319-3380.

Dates
Received: December 2014
Revised: September 2015
First available in Project Euclid: 15 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1481792587

Digital Object Identifier
doi:10.1214/16-AAP1177

Mathematical Reviews number (MathSciNet)
MR3582805

Zentralblatt MATH identifier
1362.65018

Subjects
Primary: 65C35: Stochastic particle methods [See also 82C80] 65C05: Monte Carlo methods
Secondary: 60J85: Applications of branching processes [See also 92Dxx] 47D08: Schrödinger and Feynman-Kac semigroups

Keywords
Sequential Monte Carlo rare events interacting particle systems Feynman–Kac semigroups

Citation

Cérou, Frédéric; Guyader, Arnaud. Fluctuation analysis of adaptive multilevel splitting. Ann. Appl. Probab. 26 (2016), no. 6, 3319--3380. doi:10.1214/16-AAP1177. https://projecteuclid.org/euclid.aoap/1481792587


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