V. Bogachev, T. I. Krasovitskii, S. V. Shaposhnikov
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On uniqueness of probability solutions of the Fokker-Planck-Kolmogorov equation
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.
期刊介绍：
The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in:
Mathematical analysis
Ordinary differential equations
Partial differential equations
Mathematical physics
Geometry
Algebra
Functional analysis
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