ARNAUDON, Marc; DEL MORAL, Pierre

doi:10.1214/20-EJP546

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ARNAUDON, Marc
Institut de Mathématiques de Bordeaux [IMB]

DEL MORAL, Pierre
University of New South Wales [Sydney] [UNSW]
Quality control and dynamic reliability [CQFD]

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Electronic Journal of Probability. 2020

Institute of Mathematical Statistics (IMS)

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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. This result extends the particle Gibbs samplers introduced by Andrieu-Doucet-Holenstein [2] in the context of discrete generation models to continuous time Feynman-Kac models and their interacting jump particle interpretations. We also provide new propagation of chaos estimates for continuous time genealogical tree based particle models with respect to the time horizon and the size of the systems. These results 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.< Réduire

Mots clés en anglais

Dyson-Phillips expansions

Propagation of chaos properties

Gibb- Glauber dynamics

Genealogical trees

Interacting particle systems

Feynman-Kac formulae

Ancestral lines

Gibb-Glauber dynamics

Contraction inequalities

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

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