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2020 A duality formula and a particle Gibbs sampler for continuous time Feynman-Kac measures on path spaces
Marc Arnaudon, Pierre Del Moral
Electron. J. Probab. 25: 1-54 (2020). DOI: 10.1214/20-EJP546


Continuous time Feynman-Kac measures on path spaces are central in applied probability, partial differential equation theory, as well as in quantum physics. This article presents a new duality formula between normalized Feynman-Kac distribution and their mean field particle interpretations. Among others, this formula allows us to design a reversible particle Gibbs-Glauber sampler for continuous time Feynman-Kac integration on path spaces. We also provide new Dyson-Phillips semigroup expansions, as well as novel uniform propagation of chaos estimates for continuous time genealogical tree based particle models with respect to the time horizon and the size of the systems. Our approach is self contained and it is based on a novel stochastic perturbation analysis and backward semigroup techniques. These techniques allow to obtain sharp quantitative estimates of the convergence rate to equilibrium of particle Gibbs-Glauber samplers. To the best of our knowledge these results are the first of this kind for continuous time Feynman-Kac measures.


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Marc Arnaudon. Pierre Del Moral. "A duality formula and a particle Gibbs sampler for continuous time Feynman-Kac measures on path spaces." Electron. J. Probab. 25 1 - 54, 2020.


Received: 7 November 2019; Accepted: 7 November 2020; Published: 2020
First available in Project Euclid: 24 December 2020

Digital Object Identifier: 10.1214/20-EJP546

Primary: 37L05 , 47D08 , 60H35 , 60K35

Keywords: ancestral lines , contraction inequalities , Dyson-Phillips expansions , Feynman-Kac formulae , genealogical trees , Gibb-Glauber dynamics , interacting particle systems , propagation of chaos properties


Vol.25 • 2020
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