Solutions bounded on the axis for linear inhomogeneous systems of differential equations of Ito

Main result is that for linear systems of Ito differential equations $dx(t)=A(t)x(t)dt+B(t)x(t)w(dt)+f(t)dt$, $t\in \mathbb{R}$, the bounded (in mean) solution problem is solvable for any bounded $f(t)$ only if the system is exponentially stable.