2020/12/25 by Marco Rehmeier, Rehmeier, Marco
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #58J65 #60J60 #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Statistical Mechanics and Entropy #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2012.13530
openalex publication_date 2020/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.