Fokker-Planck-Kolmogorov equations on general state spaces (A05)

• Subject Area: Mathematics
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 317210226

The aim of Project A5 is to further extend the theory of Fokker–Planck–Kolmogorov equations (FPKEs) oriented towards new applications. The emphasis on the purely analytic side is on the geometry of FPKEs, their connection to optimal transport problems, their asymptotic behavior and non-local variants of them. On the stochastic analytic side the emphasis is on nonlinear FPKEs and their probabilistic counterparts, namely nonlinear Markov processes. The research of Project A5 is structured in the following four parts: (I) Geometry of nonlinear FPKEs and connections to the Monge–Kantorovich optimal transport problem; (II) Asymptotic analysis for nonlinear FPKEs; (III) Time-fractional non-local non-linear FPKEs; (IV) Nonlinear FPKEs and nonlinear Markov process.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1283: Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications
• International Connection: China
• Applicant Institution: Universität Bielefeld
• Project Heads: Professor Dr. Michael Röckner; Professor Feng-Yu Wang