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math.AP2025
Doubling variables and uniqueness of probability solutions to degenerate stationary Kolmogorov equations
V. I. Bogachev, S. V. Shaposhnikov, D. V. Shatilovich
We obtain sufficient conditions for the uniqueness of a probability solution to the stationary Kolmogorov equation with a degenerate diffusion matrix. We employ the method of doubl…
math.AP2025
Analysis of mean field games via Fokker-Planck-Kolmogorov equations: existence of equilibria
Stanislav V. Shaposhnikov, Dmitry V. Shatilovich
We study mean field games with unbounded coefficients. The existence of a solution is proved. We propose a new approach based on Fokker-Planck-Kolmogorov equations, the Ambrosio-Fi…