Uniqueness for nonlinear Fokker–Planck equations and weak uniqueness for McKean–Vlasov SDEs

One proves the uniqueness of distributional solutions to nonlinear Fokker–Planck equations with monotone diffusion term and derive as a consequence (restricted) uniqueness in law for the corresponding McKean–Vlasov stochastic differential equation (SDE).

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Bibliographic Details
Published inStochastic partial differential equations : analysis and computations Vol. 9; no. 3; pp. 702 - 713
Main Authors Barbu, Viorel, Röckner, Michael
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2021
Springer Nature B.V
Subjects
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Differential equations
Fokker-Planck equation
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical Analysis
Partial Differential Equations
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Uniqueness
60G46
60H10
Fokker–Planck equation
60H30
Distributional solution
35C99
Mild solution
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ISSN2194-0401
2194-041X
DOI10.1007/s40072-020-00181-8

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Summary:One proves the uniqueness of distributional solutions to nonlinear Fokker–Planck equations with monotone diffusion term and derive as a consequence (restricted) uniqueness in law for the corresponding McKean–Vlasov stochastic differential equation (SDE).
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ISSN:2194-0401
2194-041X
DOI:10.1007/s40072-020-00181-8