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Convergence of U-statistics for interacting particle systems

Pierre del Moral 1, 2 Frédéric Patras 3 Sylvain Rubenthaler 3
2 ALEA - Advanced Learning Evolutionary Algorithms
CNRS - Centre National de la Recherche Scientifique : UMR5251, UB - Université de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : 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.
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Submitted on : Sunday, June 21, 2009 - 8:30:18 PM
Last modification on : Friday, February 4, 2022 - 3:30:02 AM
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  • HAL Id : inria-00397366, version 1


Pierre del Moral, Frédéric Patras, Sylvain Rubenthaler. Convergence of U-statistics for interacting particle systems. [Research Report] RR-6966, INRIA. 2009, pp.20. ⟨inria-00397366⟩



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