Geodesic
Uniqueness of a probability solution to the Kolmogorov equation with a diffusion matrix satisfying Dini’s condition
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 11-15

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In this note we study the stationary Kolmogorov equation and prove that, in the case where the diffusion matrix satisfies Dini’s condition and the drift coefficient is locally integrable to a power greater than the dimension, the ratio of two probability solutions belongs to the Sobolev class, and in the case of existence of a Lyapunov function or the global integrability of the coefficients with respect to the solution a probability solution is unique.
Keywords: Kolmogorov equation, stationary solution, uniqueness of a probability solution. 
@article{DANMA_2021_501_a1,
     author = {V. I. Bogachev and S. V. Shaposhnikov},
     title = {Uniqueness of a probability solution to the {Kolmogorov} equation with a diffusion matrix satisfying {Dini{\textquoteright}s} condition},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {11--15},
     publisher = {mathdoc},
     volume = {501},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_501_a1/}
}
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V. I. Bogachev; S. V. Shaposhnikov. Uniqueness of a probability solution to the Kolmogorov equation with a diffusion matrix satisfying Dini’s condition. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 11-15. http://geodesic.mathdoc.fr/item/DANMA_2021_501_a1/