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Coalescent tree based functional representations for some Feynman-Kac particle models

Pierre del Moral 1, 2 Frédéric Patras 2 Sylvain Rubenthaler 2
1 ASPI - Applications of interacting particle systems to statistics
UR1 - Université de Rennes 1, Inria Rennes – Bretagne Atlantique , CNRS - Centre National de la Recherche Scientifique : UMR6074
Abstract : We design a theoretic tree-based functional representation of a class of Feynman-Kac particle distributions, including an extension of the Wick product formula to interacting particle systems. These weak expansions rely on an original combinatorial, and permutation group analysis of a special class of forests. They provide refined non asymptotic propagation of chaos type properties, as well as sharp Lp-mean error bounds, and laws of large numbers for U-statistics. Applications to particle interpretations of the top eigenvalues, and the ground states of Schrödinger semigroups are also discussed.
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https://hal.inria.fr/inria-00090242
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Submitted on : Tuesday, September 5, 2006 - 6:17:19 PM
Last modification on : Thursday, January 20, 2022 - 4:13:22 PM
Long-term archiving on: : Monday, September 20, 2010 - 4:53:25 PM

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  • HAL Id : inria-00090242, version 2

Citation

Pierre del Moral, Frédéric Patras, Sylvain Rubenthaler. Coalescent tree based functional representations for some Feynman-Kac particle models. [Research Report] RR-5969, INRIA. 2006, pp.45. ⟨inria-00090242v2⟩

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