  Using the white noise setting, in particular the Wick product, the Hermite
transform, and the Kondratiev space, we present a new approach to study linear
stochastic systems, where randomness is also included in the transfer function.
We prove BIBO type stability theorems for these systems, both in the discrete
and continuous time cases. We also consider the case of dissipative systems for
both discrete and continuous time systems. We further study $\ell_1$-$\ell_2$
stability in the discrete time case, and ${\mathbf L}_2$-${\mathbf L}_\infty$
stability in the continuous time case.
