2019
Том 71
№ 5

All Issues

Krenevych A. P.

Articles: 2
Article (Ukrainian)

Asymptotic equivalence of solutions of linear Itô stochastic systems

Krenevych A. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 10. - pp. 1368–1384

We investigate the problem of the asymptotic equivalence of stochastic systems of linear ordinary equations and stochastic equations in the sense of mean square and with probability one.

Article (Ukrainian)

Investigation of exponential dichotomy of linear Itô stochastic systems with random initial data by using quadratic forms

Krenevych A. P., Stanzhitskii A. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 4. - pp. 543–553

We study conditions for the mean-square exponential dichotomy of linear Itô stochastic systems. We prove that a sufficient condition for exponential dichotomy is the existence of a quadratic form whose derivative along the solutions of a system is negative definite. The converse theorem is also proved.