Convergence of U-Statistics for Interacting Particle Systems

P. Moral (), F. Patras () and S. Rubenthaler ()
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P. Moral: Université Bordeaux I
F. Patras: Université de Nice-Sophia Antipolis
S. Rubenthaler: Université de Nice-Sophia Antipolis

Journal of Theoretical Probability, 2011, vol. 24, issue 4, 1002-1027

Abstract: 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 (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.

Keywords: Interacting particle systems; Feynman–Kac models; U-statistics; Fluctuations; Limit theorems; 82C22; 60K35; 65C35; 60F05 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10959-011-0355-6

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