2005/11/01 by Pierre Del Moral, Josselin Garnier · 2 citations
Agricultural and Biological Sciences · Engineering · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Computer science #Estimator #Event (particle physics) #Feynman diagram #Gaussian #Interacting particle system #Machine learning #Markov chain #Mathematics #Optical Network Technologies #Particle filter #Particle system #Physics #Plant and animal studies #Quantum mechanics #Rare events #Soybean genetics and cultivation #Statistical physics #Statistics #Stochastic process #math.PR #msc:60F10 #msc:62P35 #msc:65C20 #msc:65C35 #msc:68U20
paper · pdf · doi:10.1214/105051605000000566
published as Annals of Applied Probability 2005, Vol. 15, No. 4, 2496-2534 · Published at http://dx.doi.org/10.1214/105051605000000566 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2005/11/01 · arxiv created 2006/02/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.