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

Issoglio Elena, Università di Torino
Pagliarani Stefano , University of Bologna
Russo Francesco, ENSTA Paris
Trevisani Davide, Universidade da Coruña

This work 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.

Area: CS45 - Mckean-Vlasov equations and related PDEs (Elena Issoglio and Stefano Pagliarani)

Keywords: McKean-Vlasov, singular coefficients, Hörmander condition

Please Login in order to download this file