Ограниченные на оси решения линейных неоднородных систем дифференциальных уравнений Ито

Abstract

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