A second order analysis of McKean-Vlasov semigroups
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ARNAUDON, Marc | |
| hal.structure.identifier | Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP] | |
| hal.structure.identifier | Quality control and dynamic reliability [CQFD] | |
| dc.contributor.author | DEL MORAL, Pierre | |
| dc.date.accessioned | 2024-04-04T02:58:05Z | |
| dc.date.available | 2024-04-04T02:58:05Z | |
| dc.date.issued | 2020 | |
| dc.identifier.issn | 1050-5164 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192623 | |
| dc.description.abstractEn | We propose a second order differential calculus to analyze the regularity and the stability properties of the distribution semigroup associated with McKean-Vlasov diffusions. This methodology provides second order Taylor type expansions with remainder for both the evolution semigroup as well as the stochastic flow associated with this class of nonlinear diffusions. Bismut-Elworthy-Li formulae for the gradient and the Hessian of the integro-differential operators associated with these expansions are also presented. The article also provides explicit Dyson-Phillips expansions and a refined analysis of the norm of these integro-differential operators. Under some natural and easily verifiable regularity conditions we derive a series of exponential decays inequalities with respect to the time horizon. We illustrate the impact of these results with a second order extension of the Alekseev-Gröbner lemma to nonlinear measure valued semigroups and interacting diffusion flows. This second order perturbation analysis provides direct proofs of several uniform propagation of chaos properties w.r.t. the time parameter, including bias, fluctuation error estimate as well as exponential concentration inequalities. | |
| dc.language.iso | en | |
| dc.publisher | Institute of Mathematical Statistics (IMS) | |
| dc.subject.en | Taylor expansions | |
| dc.subject.en | Gradient flows | |
| dc.subject.en | Logarithmic norms | |
| dc.subject.en | Wasserstein distance | |
| dc.subject.en | Contraction inequalities | |
| dc.subject.en | Nonlinear diffusions | |
| dc.subject.en | Mean field particle systems | |
| dc.subject.en | Variational equations | |
| dc.subject.en | Bismut-Elworthy-Li formulae | |
| dc.title.en | A second order analysis of McKean-Vlasov semigroups | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1214/20-AAP1568 | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 1906.05140 | |
| bordeaux.journal | The Annals of Applied Probability | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02151808 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02151808v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=The%20Annals%20of%20Applied%20Probability&rft.date=2020&rft.eissn=1050-5164&rft.issn=1050-5164&rft.au=ARNAUDON,%20Marc&DEL%20MORAL,%20Pierre&rft.genre=article |
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