2019
Том 71
№ 10

Radchenko V. N.

Articles: 5
Article (Russian)

Heat equation and wave equation with general stochastic measures

Ukr. Mat. Zh. - 2008. - 60, № 12. - pp. 1675 – 1685

We consider the heat equation and wave equation with constant coefficients that contain a term given by an integral with respect to a random measure. Only the condition of sigma-additivity in probability is imposed on the random measure. Solutions of these equations are presented. For each equation, we prove that its solutions coincide under certain additional conditions.

Brief Communications (Russian)

Differentiability of integrals of real functions with respect to $L_0$-valued measures

Ukr. Mat. Zh. - 1999. - 51, № 11. - pp. 1582-1585

We obtain conditions for the convergence of expressions $(\mu (A))^{ - 1} \smallint _A fd\mu$ in $L_0$ as the set $A$ decreases.

Article (Russian)

Integrals of certain random functions with respect to general random measures

Ukr. Mat. Zh. - 1999. - 51, № 8. - pp. 1087–1095

For random functions that are sums of random functional series, we determine an integral over a general random measure and prove limit theorems for this integral. We consider the solution of an integral equation with respect to an unknown random measure.

Brief Communications (Russian)

Uniform integrabblity and the lebesgue theorem on convergence in $L_0$-valued measures

Ukr. Mat. Zh. - 1996. - 48, № 6. - pp. 857-860

We study integrals $∫fdμ$ of real functions over $L_0$-valued measures. We give a definition of convergence of real functions in quasimeasure and, as a special case, in $L_0$-measure. For these types of convergence, we establish conditions of convergence in probability for integrals over $L_0$-valued measures, which are analogous to the conditions of uniform integrability and to the Lebesgue theorem.

Article (Ukrainian)

Uniform integrability for integrals with respect to L0-valued measures

Ukr. Mat. Zh. - 1991. - 43, № 9. - pp. 1264–1267