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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2020 Volume 178, Pages 102–111 (Mi into615)

On solutions to Fokker–Planck equations

A. P. Mashtakov, V. A. Yumaguzhin, V. N. Yumaguzhina

Ailamazyan Program Systems Institute of Russian Academy of Sciences

Abstract: 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.

Keywords: second-order partial differential operator, jet bundle, differential invariant, equivalence problem.

UDC: 517.957, 517.958

MSC: 83C05, 83C15, 35A30, 53A55, 58J70, 58D27

DOI: 10.36535/0233-6723-2020-178-102-111



© Steklov Math. Inst. of RAS, 2025