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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierAdvanced Learning Evolutionary Algorithms [ALEA]
dc.contributor.authorDEL MORAL, Pierre
hal.structure.identifierAdvanced Learning Evolutionary Algorithms [ALEA]
hal.structure.identifierLaboratoire de Mathématiques de Versailles [LMV]
dc.contributor.authorRIO, Emmanuel
dc.date.issued2011
dc.identifier.issn1050-5164
dc.description.abstractEnThis 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.
dc.language.isoen
dc.publisherInstitute of Mathematical Statistics (IMS)
dc.subject.enConcentration inequalities
dc.subject.enmean field particle models
dc.subject.enmeasure valued processes
dc.subject.enFeynman-Kac semigroups
dc.subject.enMcKean Vlasov models.
dc.subject.enMcKean Vlasov models
dc.title.enConcentration Inequalities for Mean Field Particle Models
dc.typeArticle de revue
dc.identifier.doi10.1214/10-AAP716
dc.subject.halMathématiques [math]/Probabilités [math.PR]
bordeaux.journalThe Annals of Applied Probability
bordeaux.page1017-1052
bordeaux.volume21
bordeaux.issue3
bordeaux.peerReviewedoui
bordeaux.type.reportrr
hal.identifierinria-00375134
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//inria-00375134v1
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