Superposition principle for non-local Fokker-Planck operators

2019/10/24 by Michael Röckner, Rockner, Michael, Longjie Xie +3
Mathematics · Physics and Astronomy · #60H10 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Spectral Theory in Mathematical Physics #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1910.11022

openalex publication_date 2019/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the superposition principle for probability measure-valued solutions to non-local Fokker-Planck 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.

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