On Measure-Valued Processes Generated by Differential Equations

Authors

  • O. Yu. Feshchenko

Abstract

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 \(\Theta _t (\mu) = \mu \circ u_{\mu}^{-1} (\cdot ,t),\) where \(u_{\mu} :\mathbb{R}^d \times [0, T] \to \mathbb{R}^d\) satisfies a differential equation of a special form dependent on the measure μ. We give necessary and sufficient conditions for this representation.

Published

25.04.2003

Issue

Section

Research articles

How to Cite

Feshchenko, O. Yu. “On Measure-Valued Processes Generated by Differential Equations”. Ukrains’kyi Matematychnyi Zhurnal, vol. 55, no. 4, Apr. 2003, pp. 525-32, https://umj.imath.kiev.ua/index.php/umj/article/view/3925.