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

Pierre Del Moral; Frédéric Patras; Sylvain Rubenthaler

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

Pierre Del Moral·Frédéric Patras·Sylvain Rubenthaler

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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 $\LL\_p$-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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Pierre Del Moral, Frédéric Patras, Sylvain Rubenthaler. 2006-07-19. Coalescent tree based functional representations for some Feynman-Kac particle models. https://arxiv.org/abs/math/0607453

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