Genealogical particle analysis of rare events

Auteur : Pierre Del Moral et Josselin Garnier

• Pierre Del Moral
• Josselin Garnier

Classification AMS :65C35, 65C20, 60F10, 68U20, 62P35.

Abstract: In this paper an original interacting particle system approach is developed for study­ ing Markov chains in rare event regimes. The proposed particle system is theoretically studied through a genealogical tree interpretation of Keynman­Kac path measures. The algorithmic imple­ mentation of the particle system is presented. An e#cient estimator for the probability of ocurrence of a rare event is proposed and its variance is computed. Applications and numerical implemen­ tations 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 physi­ cally relevant problem consisting in the estimation of the outage probability due to polarization­mode dispersion in optical fibers.

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

Date: 04/05/2004

Prépublication numéro: LSP-2004-03