Abstract
We consider Kolmogorov operators with constant diffusion matrices and linear drifts, i.e., Ornstein–Uhlenbeck operators, and show that all solutions to the corresponding stationary Fokker–Planck–Kolmogorov equations (including signed solutions) are invariant measures for the generated semigroups. This also gives a relatively explicit description of all solutions.
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Funding
This work is supported by the Russian Science Foundation Grant no. 22–11–00015 at the Lomonosov Moscow State University.
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Translated from Sibirskii Matematicheskii Zhurnal, 2024, Vol. 65, No. 1, pp. 27–37. https://doi.org/10.33048/smzh.2024.65.103
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Bogachev, V.I., Shaposhnikov, S.V. Kolmogorov Equations for Degenerate Ornstein–Uhlenbeck Operators. Sib Math J 65, 21–29 (2024). https://doi.org/10.1134/S0037446624010038
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DOI: https://doi.org/10.1134/S0037446624010038