A. P. Mashtakov, V. A. Yumaguzhin, V. N. Yumaguzhina, “On solutions to Fokker–Planck equations”, Optimal control, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 178, VINITI, Moscow, 2020, 102–111
In this paper, we find necessary and sufficient conditions for existence of a transformation of independent spatial variables that transforms the Fokker–Planck equation to an equation with constant coefficients. Using these conditions, we calculate explicit solutions for two-dimensional Fokker–Planck equations. Our motivation comes from applications in image processing, where the Fokker–Planck equation typically describes blurring processes.