2019
Том 71
№ 11

All Issues

Kolomiets Yu. V.

Articles: 3
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 (Russian)

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.

Article (Ukrainian)

Averaging evolutionary equations perturbed by random processes with jumps

Kolomiets Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 2. - pp. 197–207

Weak convergence of measures generated by solutions of an evolutionary equation dependent on a small parameter to the unique solution of the martingale problem corresponding to the stochastic evolutionary equation is proved. The coefficients of the initial equation depend on random Markov processes with jumps.