Using the Chapman-Kolmogorov equation of random walks to identify drift and diffusion of the Fokker-Planck equation

A novel approach for the reconstruction of the drift and diffusion coefficients of the Fokker-Planck equation is presented. This approach is based on the Chapman-Kolmogorov equation of the inhomogeneous random walk related to the Fokker-Planck equation. Two numerical algorithms are formulated for the reconstruction problem. Results of numerical experiments demonstrate the ability of the proposed methods to solve this inverse problem also in the case of discontinuous coefficients.