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 the motion of a fluid surface. The residual acceleration field is modeled as a narrow-band noise characterized by three independent parameters: its intensity G2, a dominant frequency Ω, and a characteristic spectral width τ-1. The white noise limit corresponds to Ωτ → 0, with G2τ finite, and the limit of a periodic g jitter (or deterministic limit) can be recovered for Ωτ → ∞, G2 finite. Analysis of the linear 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 linear 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.