2009, English, Article edition: Convergence of U-statistics for interacting particle systems Del Moral, Pierre; Patras, Frédéric; Rubenthaler, Sylvain

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Physical Description
  • text
Published
  • HAL - CCSD
  • 2009
Language
  • English

Edition details

Title
  • Convergence of U-statistics for interacting particle systems
Author
  • Del Moral, Pierre
  • Patras, Frédéric
  • Rubenthaler, Sylvain
Published
  • HAL - CCSD
  • 2009
Physical Description
  • text
Subjects
Notes
  • 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.
  • HAL:inria-00397366, version 1
  • HAL:http:/​/​hal.inria.fr/​inria-00397366/​en/​
Language
  • English
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