On Asymptotic Behavior of Stochastic Differential Equation Solutions in Multidimensional Space

Consider the multidimensional SDE $\mathrm{d}X(t)=a(X(t))\mathrm{d}t+b(X(t))\mathrm{d}W(t)\mathrm{.}$ We study the asymptotic behavior of its solution $X(t)$ as $t\to \mathrm{\infty }$, namely, we study sufficient conditions of transience of its solution $X(t)$, stabilization of its multidimensional angle $X(t)\mathrm{/}\mathrm{\mid }X(t)\mathrm{\mid }$, and asymptotic equivalence of solutions of the given SDE and the following ODE without noise: $\mathrm{d}x(t)=a(x(t))\mathrm{d}t\mathrm{.}$