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On the Ambrosio-Figalli-Trevisan superposition principle for probability solutions to Fokker-Planck-Kolmogorov equations
Vladimir I. Bogachev, Michael Röckner, Stanislav V. Shaposhnikov
We prove a generalization of the known result of Trevisan on the Ambrosio-Figalli-Trevisan superposition principle for probability solutions to the Cauchy problem for the Fokker-Pl…
Log-Sobolev-type inequalities for solutions to stationary Fokker-Planck-Kolmogorov equations
V. I. Bogachev, A. V. Shaposhnikov, S. V. Shaposhnikov
We prove that every probability measure satisfying the stationary Fokker-Planck-Kolmogorov equation obtained by a -integrable perturbation of the drift term of the…
On -estimates for probability solutions to Fokker-Planck-Kolmogorov equations
Vladimir I. Bogachev, Svetlana N. Popova, Stanislav V. Shaposhnikov
We prove two new results connected with elliptic Fokker-Planck-Kolmogorov equations with drifts integrable with respect to solutions. The first result answers negatively a long-sta…
Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures
V. I. Bogachev, M. Röckner, S. V. Shaposhnikov
We study convergence in variation of probability solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary solutions. We obtain sufficient conditions for the exponent…