Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases
Arnaud Guillin, Pierre Le Bris, Pierre Monmarché
Abstract
We prove the existence of a contraction rate for Vlasov-Fokker-Planck equation in Wasserstein distance, provided the interaction potential is Lipschitz continuous and the confining potential is both (locally) Lipschitz continuous and greater than a quadratic function, thus requiring no convexity conditions. Our strategy relies on coupling methods suggested by A. Eberle [22] adapted to the kinetic setting enabling also to obtain uniform in time propagation of chaos in a non convex setting.
Topics & Concepts
Lipschitz continuityFokker–Planck equationMathematicsConvexityVlasov equationQuadratic equationConvex functionMathematical analysisRate of convergenceRegular polygonConvergence (economics)Contraction (grammar)Applied mathematicsPartial differential equationPhysicsElectronGeometryChannel (broadcasting)EngineeringEconomicsElectrical engineeringEconomic growthQuantum mechanicsInternal medicineMedicineFinancial economicsMarkov Chains and Monte Carlo MethodsStatistical Mechanics and EntropyAdvanced Thermodynamics and Statistical Mechanics