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

Abstract

We prove a version of the Ambrosio–Figalli–Trevisan superposition principle for a restricted subclass of solutions to the Fokker–Planck–Kolmogorov equation that is valid on separable infinite-dimensional Hilbert spaces. Furthermore, we transfer this restricted superposition principle into a nonlinear setting.