Project A5.1: Fokker-Planck-Kolmogorov equations on general state spaces

Summary:

The aim of the project is to further extend the theory of Fokker-Planck-Kolmogorov equations oriented towards new applications with emphasis on passing to general state spaces, including besides infinite dimensional linear spaces, in particular, infinite dimensional manifolds, configuration spaces and finally also general metric measure spaces. The intrinsic feature of our approach is to formulate a Fokker-Planck Kolmogorov equation as a partial differential equation on measures, i.e. solutions are paths of (probability) measures. This is most natural and necessary on general state spaces since there is no intrinsic reference measure available on such spaces. The project consists of three parts: (I) Fokker--Planck--Kolmogorov equations and weak uniqueness of stochastic partial differential equations; (II) Degenerate local and nonlocal Fokker-Planck-Kolmogorov equations; (III) Nonlinear Fokker-Planck-Kolmogorov equations.

Recent Preprints: