In this Note, by using the theory of stochastic differential equations (SDE), we prove uniqueness of measure-valued solutions and -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.
Dans cette Note, en utilisant la théorie des équations différentielles stochastiques (EDS), nous démontrons l'unicité de solutions 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.
Published online:
Michael Röckner 1, 2; Xicheng Zhang 3
@article{CRMATH_2010__348_7-8_435_0, author = {Michael R\"ockner and Xicheng Zhang}, title = {Weak uniqueness of {Fokker{\textendash}Planck} equations with degenerate and bounded coefficients}, journal = {Comptes Rendus. Math\'ematique}, pages = {435--438}, publisher = {Elsevier}, volume = {348}, number = {7-8}, year = {2010}, doi = {10.1016/j.crma.2010.01.001}, language = {en}, }
TY - JOUR AU - Michael Röckner AU - Xicheng Zhang TI - Weak uniqueness of Fokker–Planck equations with degenerate and bounded coefficients JO - Comptes Rendus. Mathématique PY - 2010 SP - 435 EP - 438 VL - 348 IS - 7-8 PB - Elsevier DO - 10.1016/j.crma.2010.01.001 LA - en ID - CRMATH_2010__348_7-8_435_0 ER -
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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