2017
Том 69
№ 9

All Issues

On Measure-Valued Processes Generated by Differential Equations

Feshchenko O. Yu.

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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.

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 4, pp 632-642.

Citation Example: Feshchenko O. Yu. On Measure-Valued Processes Generated by Differential Equations // Ukr. Mat. Zh. - 2003. - 55, № 4. - pp. 525-532.

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