2009/08/18 by Pierre Del Moral, Arnaud Doucet, Del Moral, Pierre +3
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Probability (math.PR) #Statistical Mechanics and Entropy #Statistics Theory (math.ST) #math.PR #math.ST #stat.CO #stat.TH
paper · pdf · doi:10.48550/arxiv.0908.2556
arxiv created 2009/08/18 · openalex publication_date 2009/08/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals "on-the-fly" as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results w.r.t. the time horizon parameter as well as functional central limit theorems and exponential concentration estimates. We also illustrate these results in the context of computational physics and imaginary time Schroedinger type partial differential equations, with a special interest in the numerical approximation of the invariant measure associated to h-processes.