A duality formula and a particle Gibbs sampler for continuous time Feynman-Kac measures on path spaces
DEL MORAL, Pierre
University of New South Wales [Sydney] [UNSW]
Quality control and dynamic reliability [CQFD]
University of New South Wales [Sydney] [UNSW]
Quality control and dynamic reliability [CQFD]
DEL MORAL, Pierre
University of New South Wales [Sydney] [UNSW]
Quality control and dynamic reliability [CQFD]
< Reduce
University of New South Wales [Sydney] [UNSW]
Quality control and dynamic reliability [CQFD]
Language
en
Article de revue
This item was published in
Electronic Journal of Probability. 2020
Institute of Mathematical Statistics (IMS)
English Abstract
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 ...Read more >
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.Read less <
English Keywords
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
Origin
Hal imported