For nonlinear stochastic Ito equations, the conditions for non-variability on the semi-axis of their solutions are studied. The corresponding sufficient conditions are given in terms of the coefficients of the equations.

1. Vetanab S. Stochastic differential equations and diffusion processes / S. Vetanab, Ikeda // Moscow: Nauka, 1986. – 445 p.
2. Mao X. Stochastic differential equations and their applications / X. Mao // Longman Scientific and Technical. – 1997. – P. 199–231.
3. Markus L. Stochastic oscillators / L. Markus, J. Weerasingle // Journal of differential equations. – 1998. – 71, N3. – P. 288–314.
4. Stanzhytskyi A. N. Asymptotic equivalence of linear stochastic Ito systems and oscillation of solutions
of linear second-order equations / A. N. Stanzhytskyi, A. P. Krenevich, I. G. Novak // Differential equations. -2011. - 47, N6. – P. 1799–813.
5. Samoilenko A. M. Qualitative and asymptotic analysis of differential equations with random perturbations / A. M. Samoilenko, O. M. Stanzhytskyi // World Scientific. - 2011. - 322 p.
6. Khas'minskiy R. Z. Stochastic stability differential equations / R. Z. Khas'minskiy // Sijthoff and Noordhoff. – 1980.
7. Milan A. Stochastic viability and comparison theorem / A. Milan // Collogium Math. Acad. Polonaise VLXVIII. – 1995. – P. 297–316.