On the Ambrosio-Figalli-Trevisan superposition principle for probability solutions to Fokker-Planck-Kolmogorov equations

We will discuss some generalizations of the known Ambrosio-Figalli-Trevisan superposition principle for probability solutions to the Cauchy problem for the Fokker-Planck-Kolmogorov equation, according to which such a solution is generated by a solution to the corresponding martingale problem. We will also discuss how the superposition principle can be useful for the study of uniqueness problems for Fokker-Planck-Kolmogorov equations with coefficients of low regularity.