# Radchenko V. N.

### 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.

### 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.

### 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.

### 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.

### Uniform integrability for integrals with respect to *L*_{0}-valued measures

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