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Ukrainian Mathematical Journal

, Volume 55, Issue 4, pp 632–642 | Cite as

On Measure-Valued Processes Generated by Differential Equations

  • O. Yu. Feshchenko
Article
  • 23 Downloads

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.

Keywords

Differential Equation Probability Measure Special Form Homogeneous Semigroup 
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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • O. Yu. Feshchenko
    • 1
  1. 1.Ukrainian State Tax AdministrationKiev

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