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Long-time behaviour and propagation of chaos for mean field kinetic particles

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  • Monmarché, Pierre

Abstract

The trend to equilibrium in large time is studied for a large particle system associated to a Vlasov–Fokker–Planck equation in the presence of a convex external potential, without smallness restriction on the interaction. From this are derived uniform in time propagation of chaos estimates, which themselves yield in turn an exponentially fast convergence for the semi-linear equation itself. The approach is quantitative.

Suggested Citation

  • Monmarché, Pierre, 2017. "Long-time behaviour and propagation of chaos for mean field kinetic particles," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1721-1737.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:6:p:1721-1737
    DOI: 10.1016/j.spa.2016.10.003
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    References listed on IDEAS

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    1. Malrieu, F., 2001. "Logarithmic Sobolev inequalities for some nonlinear PDE's," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 109-132, September.
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