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

doi:10.1007/s10959-011-0355-6

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RUBENTHALER, Sylvain
Laboratoire Jean Alexandre Dieudonné [LJAD]

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

PATRAS, Frédéric
Laboratoire Jean Alexandre Dieudonné [JAD]

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Journal of Theoretical Probability. 2011, vol. 24, n° 4, p. 1002-1027

Springer

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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 (Lee in Statistics: Textbooks and Monographs, vol. 10, Dekker, New York, 1990; de la Peña and Giné in Decoupling. Probability and Its Application, Springer, New York, 1999). 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

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Convergence of U-statistics for interacting particle systems

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