On the asymptotic stability and the boundedness of solutions of linear Ito stochastic differential equations not reduced to the Cauchy form

We consider the asymptotic stability and the boundedness with probability one of solutions of linear Ito stochastic differential equations not reduced to the Cauchy form and give some numerical examples to show that our sufficient conditions for the asymptotic stability with probability one of solutions are more general and more effective than those of Korenevskij and Mitropoloskij. Moreover, our results can also be applied to the case when the unperturbed linear deterministic system is not assumed to be stable.