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