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.
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页码：699 / 733
页数：35
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