论文标题
确定性和随机非线性fokker-Planck-Kolmogorov方程的线性化和叠加原理
Linearization and a superposition principle for deterministic and stochastic nonlinear Fokker-Planck-Kolmogorov equations
论文作者
论文摘要
我们证明了欧几里得空间上非线性fokker-planck-kolmogorov方程的叠加原理及其在Borel（子）概率度量空间上的相应线性的一阶连续性方程。结果，我们获得了这些方程式的存在和独特性结果的等效性。此外，我们证明了随机扰动的Fokker-Planck-Kolmogorov方程的类似结果。为此，我们特别表明，这种措施的随机方程与确定性情况相似，与Borel（子）概率度量空间上的线性化二阶方程本质上相关。
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.
