I have a question concerning the stability analysis for a kind of differential equation taking the form $$\dot x=Ax+Bw,$$ where $A\in \mathbb{R}^{n \times n}$, $B\in \mathbb{R}^{n \times m}$ are constant matrices and $w \in \mathbb{R}^m$ is a normal random variable, i.e., $w\sim \mathcal{N}(0,W)$ with $W$ be a symmetric and positive definite matrix.

Since the zero is not an equilibrium of the system, the Lyapunov analysis does not make sense. When the input-to-state stability analysis is considered, the robust control theory does not apply due to the unboundness of $w$. By resorting to stochastic stability in the sense of mean square or almost surely, the Ito formula seems to be invalid.

HOW to carry out the stability analysis of this kind of systems? Any pointer will be helpful. Thanks!