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
收藏
页码：699 / 733
页数：35
相关论文
共 50 条
  • [31] On Positive and Probability Solutions to the Stationary Fokker-Planck-Kolmogorov Equation
    Bogachev, V. I.
    Roeckner, M.
    Shaposhnikov, S. V.
    DOKLADY MATHEMATICS, 2012, 85 (03) : 350 - 354
  • [32] Convergence to Stationary Measures in Nonlinear Fokker-Planck-Kolmogorov Equations
    Bogachev, V. I.
    Roeckner, M.
    Shaposhnikov, S. V.
    DOKLADY MATHEMATICS, 2018, 98 (02) : 452 - 457
  • [33] Uniqueness of probability solutions to nonlinear Fokker-Planck-Kolmogorov equation
    O. A. Manita
    M. S. Romanov
    S. V. Shaposhnikov
    Doklady Mathematics, 2015, 91 : 142 - 146
  • [34] On Sobolev Classes Containing Solutions to Fokker-Planck-Kolmogorov Equations
    Bogachev, V. I.
    Popova, S. N.
    Shaposhnikov, S. V.
    DOKLADY MATHEMATICS, 2018, 98 (02) : 498 - 501
  • [35] Connection between the Fokker-Planck-Kolmogorov and nonlinear Langevin equations
    V. Ya. Fainberg
    Theoretical and Mathematical Physics, 2006, 149 : 1710 - 1725
  • [36] Estimates for Solutions to Fokker-Planck-Kolmogorov Equations with Integrable Drifts
    Bogachev, V. I.
    Shaposhnikov, A. V.
    Shaposhnikov, S. V.
    DOKLADY MATHEMATICS, 2018, 98 (03) : 559 - 563
  • [37] ON THE DISCRETIZATION OF SOME NONLINEAR FOKKER-PLANCK-KOLMOGOROV EQUATIONS AND APPLICATIONS
    Carlini, Elisabetta
    Silva, Francisco J.
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2018, 56 (04) : 2148 - 2177
  • [38] Fokker-Planck-Kolmogorov equations with a partially degenerate diffusion matrix
    Manita, O. A.
    Romanov, M. S.
    Shaposhnikov, S. V.
    DOKLADY MATHEMATICS, 2017, 96 (01) : 384 - 388
  • [39] The Fokker-Planck-Kolmogorov equation with nonlocal nonlinearity in the semiclassical approximation
    Trifonov A.Yu.
    Trifonova L.B.
    Russian Physics Journal, 2002, 45 (2) : 118 - 128
  • [40] On the Ambrosio–Figalli–Trevisan Superposition Principle for Probability Solutions to Fokker–Planck–Kolmogorov Equations
    Vladimir I. Bogachev
    Michael Röckner
    Stanislav V. Shaposhnikov
    Journal of Dynamics and Differential Equations, 2021, 33 : 715 - 739
12345