Uniform propagation of chaos and creation of chaos for a class of nonlinear diffusions
| hal.structure.identifier | Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP] | |
| hal.structure.identifier | Quality control and dynamic reliability [CQFD] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DEL MORAL, Pierre | |
| hal.structure.identifier | Probabilités, statistique, physique mathématique [PSPM] | |
| dc.contributor.author | TUGAUT, Julian | |
| dc.date.accessioned | 2024-04-04T02:57:58Z | |
| dc.date.available | 2024-04-04T02:57:58Z | |
| dc.date.issued | 2019 | |
| dc.identifier.issn | 0736-2994 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192611 | |
| dc.description.abstractEn | We 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.iso | en | |
| dc.publisher | Taylor & Francis: STM, Behavioural Science and Public Health Titles | |
| dc.subject.en | Nonlinear diffusions | |
| dc.subject.en | Propagation of chaos | |
| dc.subject.en | Feynman-Kac | |
| dc.subject.en | McKean-Vlasov models | |
| dc.subject.en | Functional inequality | |
| dc.title.en | Uniform propagation of chaos and creation of chaos for a class of nonlinear diffusions | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1080/07362994.2019.1622426 | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| bordeaux.journal | Stochastic Analysis and Applications | |
| bordeaux.page | 909-935 | |
| bordeaux.volume | 37 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 6 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02429140 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02429140v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Stochastic%20Analysis%20and%20Applications&rft.date=2019&rft.volume=37&rft.issue=6&rft.spage=909-935&rft.epage=909-935&rft.eissn=0736-2994&rft.issn=0736-2994&rft.au=DEL%20MORAL,%20Pierre&TUGAUT,%20Julian&rft.genre=article |
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