2014/11/14 by Hock Peng Chan, Pierre Del Moral, Chan, Hock Peng +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Statistical Mechanics and Entropy #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1411.3800
arxiv created 2014/11/14 · openalex publication_date 2014/11/14 · arxiv updated 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article provides a new theory for the analysis of forward and backward particle approximations of Feynman-Kac models. Such formulae are found in a wide variety of applications and their numerical (particle) approximation are required due to their intractability. Under mild assumptions, we provide sharp and non-asymptotic first order expansions of these particle methods, potentially on path space and for possibly unbounded functions. These expansions allows one to consider upper and lower bound bias type estimates for a given time horizon n and particle number N; these non-asymptotic estimates are of order O(n/N). Our approach is extended to tensor products of particle density profiles, leading to new sharp and non-asymptotic propagation of chaos estimates. The resulting upper and lower bound propagation of chaos estimates seems to be the first result of this kind for mean field particle models. As a by-product of our results, we also provide some analysis of the particle Gibbs sampler, providing first order expansions of the kernel and minorization estimates.