Genealogical particle analysis of rare events

• 成果类型: Article
• 署名作者: del Moral, P; Garnier, J
• 署名单位: Universite Cote d'Azur; Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; Sorbonne Universite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000566
• 发表日期: 2005
• 页码: 2496-2534
• 关键词: polarization mode dispersion; optical-fibers; propagation

摘要

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.