DEL MORAL, Pierre; PATRAS, Frédéric; RUBENTHALER, Sylvain

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DEL MORAL, Pierre
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]

PATRAS, Frédéric
Laboratoire Jean Alexandre Dieudonné [JAD]

RUBENTHALER, Sylvain
Laboratoire Jean Alexandre Dieudonné [JAD]

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Ce document a été publié dans

2009p. 20

Résumé en anglais

The convergence of U-statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assumption is crucial. When dealing with Feynman-Kac and other interacting particle systems of Monte Carlo type, one faces a new type of problem. Namely, in a sample of N particles obtained through the corresponding algorithms, the distributions of the particles are correlated -although any finite number of them is asymptotically independent with respect to the total number N of particles. In the present article, exploiting the fine asymptotics of particle systems, we prove convergence theorems for U-statistics in this framework.< Réduire

Project ANR

Sécurité et fiabilité des techniques de tatouages - ANR-06-SETI-0009

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Institut de Mathématiques de Bordeaux (IMB) - UMR 5251