Dieckmann, Martin: On the superposition principle for linear and nonlinear Fokker-Planck-Kolmogorov equations on Hilbert spaces. 2020
Inhalt
- Introduction
- Mathematical preliminaries
- I On the superposition principle for linear FPKEs
- Martingale problems on Hilbert spaces
- Linear FPKEs in infinite dimensions
- Superposition principle on Rd
- Framework, Equation, Solution, Assumptions
- The Ambrosio–Figalli–Trevisan superposition principle
- Generalized integrability condition
- On the superposition principle on H
- Application: stochastic Navier–Stokes equations
- Conclusion and perspective
- II On the superposition principle for nonlinear FPKEs
- Nonlinear FPKEs and MPs associated to McKean–Vlasov equations
- Nonlinear Version: Superposition principle on H
- Bibliography