Genealogical particle analysis of rare events

Details Genealogical particle analysis of rare events Genealogical particle analysis of rare events

2006-02-23

arxiv.org/abs/math/0602525v1

Annals of Applied Probability 2005, Vol. 15, No. 4, 2496-2534

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051605000000566 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051605000000566

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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