On Solutions of the Fokker–Planck Equations

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–Planc...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-10, Vol.276 (2), p.300-309
Main Authors: Mashtakov, A., Yumaguzhin, V., Yumaguzhina, V.
Format: Article
Language:English
Subjects:
Blurring
Equipment and supplies
Fokker-Planck equation
Image processing
Independent variables
Mathematical analysis
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06742-1