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.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 178, Optimal Control, 2020.
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Mashtakov, A., Yumaguzhin, V. & Yumaguzhina, V. On Solutions of the Fokker–Planck Equations. J Math Sci 276, 300–309 (2023). https://doi.org/10.1007/s10958-023-06742-1
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DOI: https://doi.org/10.1007/s10958-023-06742-1