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

被引：12

作者：

Roeckner, Michael ^{[1
]}

Xie, Longjie ^{[2
]}

Zhang, Xicheng ^{[3
]}

机构：

[1] Univ Bielefeld, Fak Math, D-33615 Bielefeld, Germany

[2] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221000, Jiangsu, Peoples R China

[3] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2020年 / 178卷 / 3-4期

关键词：

Non-local Fokker-Planck-Kolmogorov equation; Superposition principle; Martingale problem; Fractional porous media equation; PROBABILISTIC REPRESENTATION; POROUS-MEDIA; EQUATIONS; DIFFUSION; ROUGH; UNIQUENESS; DEGENERATE; SDES;

D O I：

10.1007/s00440-020-00985-8

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：699 / 733

页数：35

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