Uniqueness for nonlinear Fokker-Planck equations and weak uniqueness for McKean-Vlasov SDEs

TL;DR

This paper establishes the uniqueness of solutions for certain nonlinear Fokker-Planck equations with monotone diffusion and demonstrates the resulting weak uniqueness in law for associated McKean-Vlasov SDEs, advancing understanding of these stochastic systems.

Contribution

It proves the uniqueness of distributional solutions for nonlinear Fokker-Planck equations and derives weak uniqueness results for McKean-Vlasov SDEs, linking PDE solutions to stochastic process uniqueness.

Findings

Uniqueness of distributional solutions for nonlinear Fokker-Planck equations.

Weak uniqueness in law for McKean-Vlasov SDEs.

Extension of uniqueness results under monotone diffusion conditions.

Abstract

One proves the uniqueness of distributional solutions to nonlinear Fokker--Planck equations with monotone diffusion term and derive as a consequence (restricted) uniqueness in law for the corresponding McKean--Vlasov stochastic differential equation (SDE).