Convergence of U-statistics for interacting particle systems
| hal.structure.identifier | Laboratoire Jean Alexandre Dieudonné [LJAD] | |
| dc.contributor.author | RUBENTHALER, Sylvain | |
| hal.structure.identifier | Advanced Learning Evolutionary Algorithms [ALEA] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DEL MORAL, Pierre | |
| hal.structure.identifier | Laboratoire Jean Alexandre Dieudonné [JAD] | |
| dc.contributor.author | PATRAS, Frédéric | |
| dc.date.issued | 2011 | |
| dc.identifier.issn | 0894-9840 | |
| dc.description.abstractEn | 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 | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.title.en | Convergence of U-statistics for interacting particle systems | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s10959-011-0355-6 | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 1002.0224 | |
| bordeaux.journal | Journal of Theoretical Probability | |
| bordeaux.page | 1002-1027 | |
| bordeaux.volume | 24 | |
| bordeaux.issue | 4 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00866889 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00866889v1 | |
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