DEL MORAL, Pierre; TUGAUT, Julian

doi:10.1080/07362994.2019.1622426

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DEL MORAL, Pierre
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]

TUGAUT, Julian
Probabilités, statistique, physique mathématique [PSPM]

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Stochastic Analysis and Applications. 2019, vol. 37, n° 6, p. 909-935

Taylor & Francis: STM, Behavioural Science and Public Health Titles

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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.< Leer menos

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Nonlinear diffusions

Propagation of chaos

Feynman-Kac

McKean-Vlasov models

Functional inequality

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Uniform propagation of chaos and creation of chaos for a class of nonlinear diffusions

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