2018
Том 70
№ 9

On Measure-Valued Processes Generated by Differential Equations

Feshchenko O. Yu.

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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