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

下载

页码：699 / 733

页数：35

共 50 条

[1] Superposition principle for non-local Fokker–Planck–Kolmogorov operators
Michael Röckner
Longjie Xie
Xicheng Zhang
Probability Theory and Related Fields, 2020, 178 : 699 - 733
[2] On the Superposition Principle for Fokker-Planck-Kolmogorov Equations
Bogachev, V. I.
Roeckner, M.
Shaposhnikov, S. V.
DOKLADY MATHEMATICS, 2019, 100 (01) : 363 - 366
[3] Superposition Principle for the Fokker-Planck-Kolmogorov Equations with Unbounded Coefficients
Krasovitskii, T. I.
Shaposhnikov, S. V.
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2022, 56 (04) : 282 - 298
[4] A restricted superposition principle for (non-)linear Fokker-Planck-Kolmogorov equations on Hilbert spaces
Dieckmann, Martin
JOURNAL OF EVOLUTION EQUATIONS, 2022, 22 (02)
[5] Linearization and a superposition principle for deterministic and stochastic nonlinear Fokker-Planck-Kolmogorov equations
Rehmeier, Marco
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2023, 24 (03) : 1705 - 1739
[6] VARIATIONAL PRINCIPLE FOR FOKKER-PLANCK-KOLMOGOROV EQUATION
BOYADJIEV, TL
DOKLADI NA BOLGARSKATA AKADEMIYA NA NAUKITE, 1975, 28 (12): : 1587 - 1589
[7] On the Superposition Principle for Fokker–Planck–Kolmogorov Equations
V. I. Bogachev
M. Röckner
S. V. Shaposhnikov
Doklady Mathematics, 2019, 100 : 363 - 366
[8] On the Ambrosio-Figalli-Trevisan Superposition Principle for Probability Solutions to Fokker-Planck-Kolmogorov Equations
Bogachev, Vladimir I.
Roeckner, Michael
Shaposhnikov, Stanislav V.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2021, 33 (02) : 715 - 739
[9] FOKKER-PLANCK-KOLMOGOROV EQUATION
SMITH, JR
MATRIX AND TENSOR QUARTERLY, 1975, 25 (04): : 150 - &
[10] FOKKER-PLANCK-KOLMOGOROV EQUATION
SMITH, JR
MATRIX AND TENSOR QUARTERLY, 1975, 26 (02): : 61 - 62

← 1 2 3 4 5 →