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 \(R^d \) in the form \(Θ _t (μ) = μ ° u_μ^-1 (· ,t),\) where \(u_μ :R^d × [0, T] → R^d\) satisfies a differential equation of a special form dependent on the measure μ. We give necessary and sufficient conditions for this representation.