On Measure-Valued Processes Generated by Differential Equations - Feshchenko, O. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
We study the problem of representation of a homogeneous semigroup {Θ t } t ≥ 0 of transformations of probability measures on \(\mathbb{R}^d \) in the form \(Θ _t (μ) = μ ° u_{μ}^{-1} (· ,t),\) where \(u_{μ} :\mathbb{R}^d × [0, T] → \mathbb{R}^d\) satisfies a differential equation of a special form dependent on the measure μ. We give necessary and sufficient conditions for this representation.