An analytic approach to infinite-dimensional continuity and Fokker-Planck-Kolmogorov equations

作者：Bogachev Vladimir I^*; Da Prato Giuseppe; Roeckner Michael; Shaposhnikov Stanislav V

来源：Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 2015, 14(3): 983-1023.

We prove a new uniqueness result for solutions to Fokker-Planck-Kolmogorov (FPK) equations for probability measures on infinite-dimensional spaces. We consider infinite-dimensional drifts that admit certain finite-dimensional approximations. In contrast to much of the previous work on FPK-equations in infinite dimensions, we include cases with non-constant coefficients in the second order part and also include degenerate cases where these coefficients can even be zero. A new existence result is also proved. Some applications to FPK equations associated with SPDE's are presented.

• 出版日期2015