A Berry–Esseen theorem for Feynman–Kac and interacting particle models

2005/02/01 by Pierre Del Moral, Samy Tindel · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Target Tracking and Data Fusion in Sensor Networks #math.PR #msc:65C05 #msc:65C35 #msc:65C40

paper · pdf · doi:10.1214/105051604000000792

published as Annals of Applied Probability 2005, Vol. 15, No. 1B, 941-962 · Published at http://dx.doi.org/10.1214/105051604000000792 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2005/02/01 · arxiv created 2005/03/24 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate the speed of convergence of the fluctuations of a general class of Feynman–Kac particle approximation models. We design an original approach based on new Berry–Esseen type estimates for abstract martingale sequences combined with original exponential concentration estimates of interacting processes. These results extend the corresponding statements in the classical theory and apply to a class of branching and genealogical path-particle models arising in nonlinear filtering literature as well as in statistical physics and biology.

Cited by

• Genealogical particle analysis of rare events

Related

• A Sharp First Order Analysis of Feynman-Kac Particle Models
• Berry-Esseen estimates for regenerative processes under weak moment assumptions
• A Backward Particle Interpretation of Feynman-Kac Formulae
• A Berry-Esseen bound with (almost) sharp dependence conditions
• Rate of convergence of the Kac-like particle system