Abstract: | We prove the superposition principle for probability measure-valued solutions to non-local Fokker-Planck-Kolmogorov equations, which in turn yields the equivalence between martingale problems for SDEs with jumps and such non-local PDEs with rough coefficients. As an application, we obtain a probabilistic representation for weak solutions of fractional porous media equations (This is a joint work with Michael Rockner and Longjie Xie). |