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hal.structure.identifierCentre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
hal.structure.identifierQuality control and dynamic reliability [CQFD]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorDEL MORAL, Pierre
hal.structure.identifierProbabilités, statistique, physique mathématique [PSPM]
dc.contributor.authorTUGAUT, Julian
dc.date.accessioned2024-04-04T02:57:58Z
dc.date.available2024-04-04T02:57:58Z
dc.date.issued2019
dc.identifier.issn0736-2994
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192611
dc.description.abstractEnWe are interested in nonlinear diffusions in which the own law intervenes in the drift. This kind of diffusions corresponds to the hydrodynamical limit of some particle system. One also talks about propagation of chaos. It is well known, for McKean-Vlasov diffusions, that such a propagation of chaos holds on finite-time interval. We here aim to establish a uniform propagation of chaos even if the external force is not convex, with a diffusion coefficient sufficiently large. The idea consists in combining the propagation of chaos on a finite-time interval with a functional inequality, already used by Bolley, Gentil and Guillin. Here, we also deal with a case in which the system at time t = 0 is not chaotic and we show under easily checked assumptions that the system becomes chaotic as the number of particles goes to infinity together with the time. This yields the first result of this type for mean field particle diffusion models as far as we know.
dc.language.isoen
dc.publisherTaylor & Francis: STM, Behavioural Science and Public Health Titles
dc.subject.enNonlinear diffusions
dc.subject.enPropagation of chaos
dc.subject.enFeynman-Kac
dc.subject.enMcKean-Vlasov models
dc.subject.enFunctional inequality
dc.title.enUniform propagation of chaos and creation of chaos for a class of nonlinear diffusions
dc.typeArticle de revue
dc.identifier.doi10.1080/07362994.2019.1622426
dc.subject.halMathématiques [math]/Probabilités [math.PR]
bordeaux.journalStochastic Analysis and Applications
bordeaux.page909-935
bordeaux.volume37
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue6
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02429140
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02429140v1
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