Tree based functional expansions for Feynman--Kac particle models

Abstract

We design exact polynomial expansions of a class of Feynman--Kac particle distributions. These expansions are finite and are parametrized by coalescent trees and other related combinatorial quantities. The accuracy of the expansions at any order is related naturally to the number of coalescences of the trees. Our results include an extension of the Wick product formula to interacting particle systems. They also provide refined nonasymptotic propagation of chaos-type properties, as well as sharp ${\mathbb{L}}_p$-mean error bounds, and laws of large numbers for $U$-statistics.

Published in at http://dx.doi.org/10.1214/08-AAP565 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
• Combinatorial aspects of matrix models

Cited by in corpus (9)

• Stability properties of some particle filters
• Linear Variance Bounds for Particle Approximations of Time-Homogeneous Feynman-Kac Formulae
• On the Stability of Sequential Monte Carlo Methods in High Dimensions
• CLT for U-statistics of Ornstein-Uhlenbeck branching particle system with small branching rate
• On particle Gibbs Markov chain Monte Carlo models
• Automatic Backward Filtering Forward Guiding for Markov processes and graphical models
• A Sharp First Order Analysis of Feynman-Kac Particle Models
• Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean
• A second order analysis of McKean-Vlasov semigroups