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Continuous time Feynman-Kac measures on path spaces are central in appliedprobability, partial differential equation theory, as well as in quantumphysics. This article presents a new duality formula between normalizedFeynman-Kac distribution and their mean field particle interpretations. Amongothers, this formula allows us to design a reversible particle Gibbs-Glaubersampler for continuous time Feynman-Kac integration on path spaces. This resultextends the particle Gibbs samplers introduced by Andrieu-Doucet-Holenstein [2]in the context of discrete generation models to continuous time Feynman-Kacmodels and their interacting jump particle interpretations. We also provide newpropagation of chaos estimates for continuous time genealogical tree basedparticle models with respect to the time horizon and the size of the systems.These results allow to obtain sharp quantitative estimates of the convergencerate to equilibrium of particle Gibbs-Glauber samplers. To the best of ourknowledge these results are the first of this kind for continuous timeFeynman-Kac measures.

A duality formula and a particle Gibbs sampler for continuous time Feynman-Kac measures on path spaces