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

Michael Röckner; Longjie Xie; Xicheng Zhang

doi:10.1007/s00440-020-00985-8

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

Michael Röckner, Longjie Xie, Xicheng Zhang^*

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

14 引用（Scopus）

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.

源语言	英语
页（从-至）	699-733
页数	35
期刊	Probability Theory and Related Fields
卷	178
期	3-4
DOI	https://doi.org/10.1007/s00440-020-00985-8
出版状态	已出版 - 1 12月 2020
已对外发布	是

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Röckner, M., Xie, L., & Zhang, X. (2020). Superposition principle for non-local Fokker–Planck–Kolmogorov operators. Probability Theory and Related Fields, 178(3-4), 699-733. https://doi.org/10.1007/s00440-020-00985-8

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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.",

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

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