A stochastic model is derived from wind stress and bottom pressure gauge data to examine the response of the Antarctic Circumpolar Current (ACC) transport to wind stress forcing. A general method is used to estimate the drift and diffusion coefficients of a continuous stationary Markovian system. As a first approximation, the response of the ACC to wind stress forcing can be described by a multivariate Ornstein-Uhlenbeck process: Gaussian red noise wind stress drives the evolution of the ACC transport, which is damped by a linear drag term. The model indicates that about 30(±10)% of ACC variability is directly driven by the wind stress. This stochastic model can serve as a null hypothesis for studies of wind driven ACC variability. A more accurate stochastic description of the wind stress over the Southern Ocean requires a multiplicative noise component. The variability of the wind stress increases approximately linearly with increasing wind stress values. A multiplicative stochastic process generates a power-law distribution rather than a Gaussian distribution. A simple stochastic model shows that non-Gaussian forcing could have a significant impact on the velocity (or transport) probability density functions (PDFs) of the wind-driven circulation. The net oceanic damping determines whether the distribution of the oceanic flow is Gaussian (small damping) or resembles the distribution of the atmospheric forcing (large damping).