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Matematicheskie Zametki, 2024, Volume 115, Issue 3, Pages 466–480
DOI: https://doi.org/10.4213/mzm14100 (Mi mzm14100) 		 
Khas'minskii's Theorem for the Kolmogorov Equation with Partially Singular Diffusion Matrix

S. V. Shaposhnikov, D. V. Shatilovich

Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm14100
Abstract: The stationary Kolmogorov equation with partially singular diffusion matrix and discontinuous drift coefficient is studied. Sufficient conditions for the existence of a probabilistic solution are obtained. Examples demonstrating the sharpness of these conditions are given.
Keywords: Kolmogorov equation, invariant measure of a diffusion process, Lyapunov function.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-284
Contest «Young Russian Mathematics»
This work was supported by the Ministry of Science and Higher Education of the Russian Federation in the framework of the program of Moscow Center for Fundamental and Applied Mathematics (contract no. 075-15-2022-284). S. V. Shaposhnikov is a winner of the competition “Young Mathematics of Russia” and thanks its jury and sponsors.
Received: 08.07.2023
English version:
Mathematical Notes, 2024, Volume 115, Issue 3, Pages 427–438
DOI: https://doi.org/10.1134/S0001434624030155
Bibliographic databases:
Document Type: Article
UDC: 519.217.4+517.956.226
MSC: 35A01
Language: Russian
Citation: S. V. Shaposhnikov, D. V. Shatilovich, “Khas'minskii's Theorem for the Kolmogorov Equation with Partially Singular Diffusion Matrix”, Mat. Zametki, 115:3 (2024), 466–480; Math. Notes, 115:3 (2024), 427–438
Citation in format AMSBIB
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\paper Khas'minskii's Theorem for the Kolmogorov Equation
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\yr 2024
\vol 115
\issue 3
\pages 466--480
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\crossref{https://doi.org/10.4213/mzm14100}
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\transl
\jour Math. Notes
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\pages 427--438
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