Convergence of \(U\)-statistics for interacting particle systems
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Publication:662874
DOI10.1007/S10959-011-0355-6zbMATH Open1233.82025arXiv1002.0224OpenAlexW2042399590MaRDI QIDQ662874
Author name not available (Why is that?)
Publication date: 13 February 2012
Published in: (Search for Journal in Brave)
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 [Lee90, de99]. 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.
Full work available at URL: https://arxiv.org/abs/1002.0224
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