Superposition principle for non-local Fokker-Planck-Kolmogorov operators

• 成果类型: Article
• 署名作者: Roeckner, Michael; Xie, Longjie; Zhang, Xicheng
• 署名单位: University of Bielefeld; Jiangsu Normal University; Wuhan University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-020-00985-8
• 发表日期: 2020
• 页码: 699-733
• 关键词: probabilistic representation; porous-media; EQUATIONS; diffusion; rough; uniqueness; degenerate; sdes

摘要

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.