Modèle d'îlots de particules et application en fiabilité
Christelle Vergé · HAL (Le Centre pour la Communication Scientifique Directe) · 2015
Feynman-Kac models (which generalize hidden Markov models) are nowadays widely used as they allow to model a large variety of time series in several fields such as aeronautics, rare event analysis, signal processing, finance, biology, and so on. Different approximations based on Monte Carlo principles have been developed as Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC). In this thesis, we focus on SMC methods. They consist in approximating a targeted law through an interacting particle system sequentially defined. Numerous algorithms have been developed and studied in the literature.We propose techniques of parallelization of such SMC methods, considering subpopulations of particles referred to by us as islands which can also interact.We study convergence properties of these island particle algorithms.Especially, we prove a central limit theorem (CLT) and the stability of the variance, thanks to exponential deviation inequality and triangular arrays dened on the island level. We also propose a novel algorithm of interacting island particles to estimate the law of random parameters conditionally to a rare event. We illustrate its convergence and we apply it to two critical cases in aerospace.