Journal Articles Electronic Journal of Probability Year : 2022

Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases

Abstract

We prove the existence of a contraction rate for Vlasov-Fokker-Planck equation in Wasserstein distance, provided the interaction potential is (locally) Lipschitz continuous and the confining potential is both Lipschitz continuous and greater than a quadratic function, thus requiring no convexity conditions. Our strategy relies on coupling methods suggested by A. Eberle adapted to the kinetic setting enabling also to obtain uniform in time propagation of chaos in a non convex setting.
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Dates and versions

hal-03323156 , version 1 (20-08-2021)

Identifiers

  • HAL Id : hal-03323156 , version 1

Cite

Arnaud Guillin, Pierre Le Bris, Pierre Monmarché. Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases. Electronic Journal of Probability, 2022, 27, pp.144. ⟨hal-03323156⟩
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