Comptes Rendus
no. 7-8
Probability Theory
Weak uniqueness of Fokker–Planck equations with degenerate and bounded coefficients
[Unicité faible des équations de Fokker–Planck avec coefficients dégénérées et bornées]

Présenté par : Paul Malliavin

Michael Röckner1, 2 ; Xicheng Zhang3
1 Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
2 Departments of Mathematics and Statistics, Purdue University, W. Laffayette, IN 47907, USA
3 Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China
Comptes Rendus. Mathématique, Volume 348 (2010) no. 7-8, pp. 435-438.

Dans cette Note, en utilisant la théorie des équations différentielles stochastiques (EDS), nous démontrons l'unicité de solutions Lp et à valeurs mesures pour des équations de Fokker–Planck du second ordre dégénérées, sous des conditions faibles sur les coefficients. Nos résultats d'unicité sont fondés sur le lien naturel existant entre les équations de Fokker–Planck et les EDS.

In this Note, by using the theory of stochastic differential equations (SDE), we prove uniqueness of measure-valued solutions and Lp-solutions to degenerate second order Fokker–Planck equations under weak conditions on the coefficients. Our uniqueness results are based on the natural connection between Fokker–Planck equations and SDEs.

Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.01.001
Michael Röckner 1, 2 ; Xicheng Zhang 3

1 Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
2 Departments of Mathematics and Statistics, Purdue University, W. Laffayette, IN 47907, USA
3 Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China 
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Michael Röckner; Xicheng Zhang. Weak uniqueness of Fokker–Planck equations with degenerate and bounded coefficients. Comptes Rendus. Mathématique, Volume 348 (2010) no. 7-8, pp. 435-438. doi : 10.1016/j.crma.2010.01.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.01.001/

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