2019
Том 71
№ 8

All Issues

Feshchenko O. Yu.

Articles: 2
Article (Ukrainian)

On Measure-Valued Processes Generated by Differential Equations

Feshchenko O. Yu.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 4. - pp. 525-532

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.

Article (Ukrainian)

Stochastic Semigroups and Random Mass Transfer

Feshchenko O. Yu.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 9. - pp. 1251-1259

We consider the problem of random mass transfer on a metric compactum defined by a purely discontinuous stochastic semigroup \(T_t^s\) . We give a description of this semigroup based on a Markov process with random transition probability. We present conditions for the independence of measure-valued processes of the form \(T_t^0 {\mu}_{0}\) , depending on the initial mass μ0.