Degenerate McKean-Vlasov equations with drift in anisotropic negative Besov spaces

Elena Issoglio, Stefano Pagliarani, Francesco Russo and 
Davide Trevisani
Publication type:
Paper in peer-reviewed journals
assets/images/icons/icon_arxiv.png 2401.09165
Keywords :
Stochastic differential equations; McKean-Vlasov; kinetic PDEs; martingale problem; singular drift; anisotropic Besov-Hölder spaces; Schauder estimates.;
The paper is concerned with a McKean-Vlasov type SDE with drift in anisotropic Besov spaces with negative regularity and with degenerate diffusion matrix under the weak Hörmander condition. The main result is of existence and uniqueness of a solution in law for the McKean-Vlasov equation, which is formulated as a suitable martingale problem. All analytical tools needed are derived in the paper, such as the well-posedness of the Fokker-Planck and Kolmogorov PDEs with distributional drift, as well as continuity dependence on the coefficients. The solutions to these PDEs naturally live in anisotropic Besov spaces, for which we developed suitable analytical inequalities, such as Schauder estimates.
    author={Elena Issoglio and Stefano Pagliarani and Francesco Russo and 
           Davide Trevisani },
    title={Degenerate McKean-Vlasov equations with drift in anisotropic 
           negative Besov spaces },
    year={submitted },