Estimates of distances between solutions of Fokker--Planck--Kolmogorov equations with partially degenerate diffusion matrices

Oxana A. Manita, Maxim S. Romanov, Stanislav V. Shaposhnikov
Theory of Stochastic Processes
Vol.23 (39), no.2, 2018, pp.41-54
Using a metric which interpolates between the Kantorovich metric and the total variation norm we estimate the distance between solutions to Fokker--Planck--Kolmogorov equations with degenerate diffusion matrices. Some relations between the degeneracy of the diffusion matrix and the regularity of the drift coefficient are analysed. Applications to nonlinear Fokker-Planck-Kolmogorov equations are given.