Geodesic
On solutions to Fokker--Planck equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Optimal control, Tome 178 (2020), pp. 102-111

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{INTO_2020_178_a7,
     author = {A. P. Mashtakov and V. A. Yumaguzhin and V. N. Yumaguzhina},
     title = {On solutions to {Fokker--Planck} equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {102--111},
     publisher = {mathdoc},
     volume = {178},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_178_a7/}
}
TY  - JOUR
AU  - A. P. Mashtakov
AU  - V. A. Yumaguzhin
AU  - V. N. Yumaguzhina
TI  - On solutions to Fokker--Planck equations
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2020
SP  - 102
EP  - 111
VL  - 178
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2020_178_a7/
LA  - ru
ID  - INTO_2020_178_a7
ER  - 
%0 Journal Article
%A A. P. Mashtakov
%A V. A. Yumaguzhin
%A V. N. Yumaguzhina
%T On solutions to Fokker--Planck equations
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2020
%P 102-111
%V 178
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2020_178_a7/
%G ru
%F INTO_2020_178_a7
A. P. Mashtakov; V. A. Yumaguzhin; V. N. Yumaguzhina. On solutions to Fokker--Planck equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Optimal control, Tome 178 (2020), pp. 102-111. http://geodesic.mathdoc.fr/item/INTO_2020_178_a7/