inria-00397366, version 1
Convergence of U-statistics for interacting particle systems
Pierre Del Moral
1, 2Frédéric Patras
3Sylvain Rubenthaler
a, 3
N° RR-6966 (2009)
Résumé : 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.
- a – Université de Nice Sophia-Antipolis
- 1 : Institut de Mathématiques de Bordeaux (IMB)
- CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
- 2 : ALEA (INRIA Bordeaux - Sud-Ouest)
- INRIA – Université de Bordeaux – CNRS : UMR5251
- 3 : Laboratoire Jean Alexandre Dieudonné (JAD)
- CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS)
- Domaine : Mathématiques/Probabilités
- Référence interne : RR-6966
- inria-00397366, version 1
- http://hal.inria.fr/inria-00397366
- oai:hal.inria.fr:inria-00397366
- Contributeur : Pierre Del Moral
- Soumis le : Dimanche 21 Juin 2009, 20:30:18
- Dernière modification le : Jeudi 29 Octobre 2009, 10:56:03






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