@article{463ca7b1273841d9aedc25db5df2473b,
title = "Superposition principle for non-local Fokker–Planck–Kolmogorov operators",
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 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.",
keywords = "Fractional porous media equation, Martingale problem, Non-local Fokker–Planck–Kolmogorov equation, Superposition principle",
author = "Michael R{\"o}ckner and Longjie Xie and Xicheng Zhang",
note = "Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2020",
month = dec,
day = "1",
doi = "10.1007/s00440-020-00985-8",
language = "English",
volume = "178",
pages = "699--733",
journal = "Probability Theory and Related Fields",
issn = "0178-8051",
publisher = "Springer New York",
number = "3-4",
}