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 stochastic differential equations with jumps and such non-local partial differential equations with rough coefficients. As an application, we obtain a probabilistic representation for weak solutions of fractional porous media equations.

中文翻译：

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非局部 Fokker-Planck-Kolmogorov 算子的叠加原理

我们证明了非局部 Fokker-Planck-Kolmogorov 方程的概率测度值解的叠加原理，这反过来又产生了具有跳跃的随机微分方程的鞅问题与这种具有粗糙系数的非局部偏微分方程之间的等价性。作为一个应用，我们获得了分数多孔介质方程弱解的概率表示。