A sharp first order analysis of Feynman-Kac particle models, Part I: Propagation of chaos

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Del Moral, Pierre^1,2  Jasra, Ajay³ 

[1] Univ Bordeaux 1, Ctr INRIA Bordeaux Sud Ouest, FR-33405 Talence, France

[2] Univ Bordeaux 1, Inst Math Bordeaux, FR-33405 Talence, France

[3] Natl Univ Singapore, Dept Stat & Appl Probabil & Appl Proba, SG-117546 Singapore, Singapore

关键词: Feynman-Kac formulae;    Particle simulation;    Propagation of chaos;   

DOI  :  10.1016/j.spa.2017.04.007

来源: Elsevier

【 摘 要 】

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 is 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 allow 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 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 propagations of chaos estimates seem to be the first result of this kind for mean field particle models. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free