The Annals of Applied Probability

Genealogical particle analysis of rare events

Pierre Del Moral and Josselin Garnier

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Abstract

In this paper an original interacting particle system approach is developed for studying Markov chains in rare event regimes. The proposed particle system is theoretically studied through a genealogical tree interpretation of Feynman–Kac path measures. The algorithmic implementation of the particle system is presented. An estimator for the probability of occurrence of a rare event is proposed and its variance is computed, which allows to compare and to optimize different versions of the algorithm. Applications and numerical implementations are discussed. First, we apply the particle system technique to a toy model (a Gaussian random walk), which permits to illustrate the theoretical predictions. Second, we address a physically relevant problem consisting in the estimation of the outage probability due to polarization-mode dispersion in optical fibers.

Article information

Source
Ann. Appl. Probab., Volume 15, Number 4 (2005), 2496-2534.

Dates
First available in Project Euclid: 7 December 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1133965770

Digital Object Identifier
doi:10.1214/105051605000000566

Mathematical Reviews number (MathSciNet)
MR2187302

Zentralblatt MATH identifier
1097.65013

Subjects
Primary: 65C35: Stochastic particle methods [See also 82C80] 65C20: Models, numerical methods [See also 68U20] 60F10: Large deviations 68U20: Simulation [See also 65Cxx] 62P35: Applications to physics

Keywords
Rare events Monte Carlo Markov chains importance sampling interacting particle systems genetic algorithms

Citation

Del Moral, Pierre; Garnier, Josselin. Genealogical particle analysis of rare events. Ann. Appl. Probab. 15 (2005), no. 4, 2496--2534. doi:10.1214/105051605000000566. https://projecteuclid.org/euclid.aoap/1133965770


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References

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