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mean field particle algorithms

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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A backward particle interpretationof Feynman-Kac formulae
Pierre Del Moral, Arnaud Doucet, Sumeetpal S. Singh
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 44 / Issue 5 / September 2010

Published online by Cambridge University Press:

26 August 2010, pp. 947-975

Print publication:

September 2010
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We design a particle interpretation of Feynman-Kac measures on path spacesbased on a backward Markovian representation combined with a traditionalmean field particle interpretation of the flow of their final timemarginals. In contrast to traditional genealogical tree based models, thesenew particle algorithms can be used to compute normalized additivefunctionals “on-the-fly” as well as theirlimiting occupation measures with a given precision degree that does notdepend on the final time horizon.We provide uniform convergence results w.r.t. the time horizon parameter aswell as functional central limit theorems and exponential concentrationestimates, yielding what seems to be the first results of this type for thisclass of models. We also illustrate these results in the context offiltering of hidden Markov models, as well as in computational physics andimaginary time Schroedinger type partial differential equations, with aspecial interest in the numerical approximation of the invariant measureassociated to h-processes.