A duality formula for Feynman-Kac path particle models

This Note and its extended version [10] present a new duality formula between genetic type genealogical tree based particle models and Feynman-Kac measures on path spaces. Among others, this formula allows us to design reversible Gibbs-Glauber Markov chains for Feynman-Kac integration on path spaces. Our approach yields new Taylor series expansions of the particle Gibbs-Glauber semigroup around its equilibrium measure w.r.t. the size of the particle system, generalizing the recent work of Andrieu, Doucet, and Holenstein [1]. We analyze the rate of convergence to equilibrium in terms of the ratio of the length of the trajectories to the number of particles. The analysis relies on a tree-based functional and combinatorial representation of a class of Feynman-Kac particle models with a frozen ancestral line. We illustrate the impact of these results in the context of Quantum and Diffusion Monte Carlo methods. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.