A restricted superposition principle for (non-)linear Fokker-Planck-Kolmogorov equations on Hilbert spaces.

We carefully combine three well-known results to ensure joint existence of solutions to Fokker-Planck-Kolmogorov equations and martingale problems allowing us to derive a version (covering a restricted subclass of solutions) of the Ambrosio-Figalli-Trevisan superposition principle that is valid on separable infinite-dimensional Hilbert spaces. Furthermore, we transfer this restricted superposition principle into a nonlinear setting.