The Annals of Applied Probability

Genealogical particle analysis of rare events

Pierre Del Moral and Josselin Garnier

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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.

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

First available in Project Euclid: 7 December 2005

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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

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


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

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