  We present a perturbation method for determining the moment stability of
linear ordinary differential equations with parametric forcing by colored
noise. In particular, the forcing arises from passing white noise through an
$n$th order filter. We carry out a perturbation analysis based on a small
parameter $\varepsilon$ that gives the amplitude of the forcing. Our
perturbation analysis is based on a ladder operator approach to the vector
Ornstein-Uhlenbeck process. We can carry out our perturbation expansion to any
order in $\varepsilon$, for a large class linear filters, and for quite
arbitrary linear systems. As an example we apply our results to the
stochastically forced Mathieu equation.
