On the discretization of some nonlinear Fokker-Planck-Kolmogorov equations and applications
In this work, we consider the discretization of some nonlinear Fokker-Planck-Kolmogorov equations. The scheme we propose preserves the nonnegativity of the solution, conserves the mass, and, as the discretization parameters tend to zero, has limit measure-valued trajectories which are shown to solve the equation. The main assumptions to obtain a convergence result are that the coefficients are continuous and satisfy a suitable linear growth property with respect to the space variable. In particular, we obtain a new proof of existence of solutions for such equations.