A backward particle interpretation of Feynman-Kac formulae

Del Moral, Pierre; Doucet, Arnaud; Singh, Sumeetpal S.

ESAIM: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 5, pp. 947-975.

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals “on-the-fly” as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results w.r.t. the time horizon parameter as well as functional central limit theorems and exponential concentration estimates, yielding what seems to be the first results of this type for this class of models. We also illustrate these results in the context of filtering of hidden Markov models, as well as in computational physics and imaginary time Schroedinger type partial differential equations, with a special interest in the numerical approximation of the invariant measure associated to h-processes.

Classification : 65C05, 65C35, 60G35, 47D08
Mots clés : Feynman-Kac models, mean field particle algorithms, functional central limit theorems, exponential concentration, non asymptotic estimates

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