On uniqueness of probability solutions of the Fokker-Planck-Kolmogorov equation

V. I. Bogachev   ; T. I. Krasovitskii   ; S. V. Shaposhnikov

Sbornik. Mathematics, Tome 212 (2021) no. 6, pp. 745-781

Résumé

The paper gives a solution to the long-standing problem of uniqueness for probability solutions to the Cauchy problem for the Fokker-Planck-Kolmogorov equation with an unbounded drift coefficient and unit diffusion coefficient. It is proved that in the one-dimensional case uniqueness holds and in all other dimensions it fails. The case of nonconstant diffusion coefficients is also investigated. Bibliography: 70 titles.

Détail

Keywords: Cauchy problem, uniqueness problem.
Mots-clés : Fokker-Planck-Kolmogorov equation

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