Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 178, Pages 102–111
DOI: https://doi.org/10.36535/0233-6723-2020-178-102-111 (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
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DOI: https://doi.org/10.36535/0233-6723-2020-178-102-111
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.
Funding agency Grant number
Russian Science Foundation 17-11-01387
The work of A. P. Mashtakov and V. A. Yumaguzhin was supported by the Russian Science Foundation (project № 17-11-01387).
Document Type: Article
UDC: 517.957, 517.958
MSC: 83C05, 83C15, 35A30, 53A55, 58J70, 58D27
Language: Russian
Citation: A. P. Mashtakov, V. A. Yumaguzhin, V. N. Yumaguzhina, “On solutions to Fokker–Planck equations”, Optimal control, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 178, VINITI, Moscow, 2020, 102–111
Citation in format AMSBIB
\Bibitem{MasYumYum20}
\by A.~P.~Mashtakov, V.~A.~Yumaguzhin, V.~N.~Yumaguzhina
\paper On solutions to Fokker--Planck equations
\inbook Optimal control
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 178
\pages 102--111
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into615}
\crossref{https://doi.org/10.36535/0233-6723-2020-178-102-111}
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