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.