Concentration Inequalities for Mean Field Particle Models

Pierre Del Moral 1, 2, * Emmanuel Rio 2, 3
* Auteur correspondant
2 ALEA - Advanced Learning Evolutionary Algorithms
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of non linear measure valued processes. We combine an original stochastic perturbation analysis with a concentration analysis for triangular arrays of conditionally independent random sequences, which may be of independent interest. Under some additional stability properties of the limiting measure valued processes, uniform concentration properties with respect to the time parameter are also derived. The concentration inequalities presented here generalize the classical Hoeffding, Bernstein and Bennett inequalities for independent random sequences to interacting particle systems, yielding very new results for this class of models. We illustrate these results in the context of McKean Vlasov type diffusion models, McKean collision type models of gases, and of a class of Feynman-Kac distribution flows arising in stochastic engineering sciences and in molecular chemistry.
Type de document :
Article dans une revue
The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2011, 21 (3), pp.1017-1052. 〈10.1214/10-AAP716〉
Liste complète des métadonnées

Littérature citée [10 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/inria-00375134
Contributeur : Pierre Del Moral <>
Soumis le : dimanche 26 avril 2009 - 18:20:09
Dernière modification le : jeudi 11 janvier 2018 - 06:25:42
Document(s) archivé(s) le : samedi 26 novembre 2016 - 08:31:56

Fichier

RR-6901.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Pierre Del Moral, Emmanuel Rio. Concentration Inequalities for Mean Field Particle Models. The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2011, 21 (3), pp.1017-1052. 〈10.1214/10-AAP716〉. 〈inria-00375134v3〉

Partager

Métriques

Consultations de la notice

637

Téléchargements de fichiers

249