2019
Том 71
№ 6

All Issues

Kolomiets Yu. V.

Articles: 2
Article (Russian)

On weak convergence of solutions of random perturbed evolution equations

Kolomiets Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 2. - pp. 213–219

We consider the weak convergence of measures generated by solutions of linear evolution equations depending on diffusion processes to the Gaussian measure as a small parameter tends to zero.

Article (Ukrainian)

Averaging of randomly perturbed evolutionary equations

Kolomiets Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 963–971

Evolutionary equations with coefficients perturbed by diffusion processes are considered. It is proved that the solutions of these equations converge weakly in distribution, as a small parameter tends to zero, to a unique solution of a martingale problem that corresponds to an evolutionary stochastic equation in the case where the powers of a small parameter are inconsistent.