Linearization and a superposition principle for deterministic and stochastic nonlinear Fokker-Planck-Kolmogorov equations

Understand

We prove a superposition principle for nonlinear Fokker-Planck-Kolmogorov equations on Euclidean spaces and their corresponding linearized first-order continuity equation over the space of Borel (sub-)probability measures.

• As a consequence, we obtain equivalence of existence and uniqueness results for these equations.
• Moreover, we prove an analogous result for stochastically perturbed Fokker-Planck-Kolmogorov equations.
• To do so, we particularly show that such stochastic equations for measures are, similarly to the deterministic case, intrinsically related to linearized second-order equations on the space of Borel (sub-)probability measures.