  We introduce a stochastic model to analyze in quantitative detail the effect
of the high frequency components of the residual accelerations onboard
spacecraft (often called g-jitter) on fluid motion. The residual acceleration
field is modeled as a narrow band noise characterized by three independent
parameters: its intensity $G^{2}$, a dominant frequency $\Omega$, and a
characteristic spectral width $\tau^{-1}$. The white noise limit corresponds to
$\Omega \tau \rightarrow 0$, with $G^{2} \tau$ finite, and the limit of a
periodic g-jitter (or deterministic limit) can be recovered for $\Omega \tau
\rightarrow \infty$, $G^{2}$ finite. The analysis of the response of a fluid
surface subjected to a fluctuating gravitational field leads to the stochastic
Mathieu equation driven by both additive and multiplicative noise. We discuss
the stability of the solutions of this equation in the two limits of white
noise and deterministic forcing, and in the general case of narrow band noise.
The results are then applied to typical microgravity conditions.
