An analytic approach to infinite-dimensional continuity and fokker-planck-kolmogorov equations

Bogachev VI, Da Prato G, Röckner M, Shaposhnikov SV. An analytic approach to infinite-dimensional continuity and fokker-planck-kolmogorov equations. 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