  The mean-field dynamics of a particle in a random, but short range correlated
potential, offers the opportunity of observing both aging and driven stationary
regimes. Using a geometrical approach previously introduced by the author, we
study here the relation between these two situations, in the pure relaxational
limit, i.e. the zero temperature case. In the stationary regime, the
velocity(v) -force(f) characteristics is a power law, while the characteristic
times scale like powers of v, in agreement with an early proposal by Horner.
The cross-over between the aging, linear-response regime and the non linear
stationary regime is smooth, and we propose a parametrisation of the
correlation functions valid in both cases, by means of an "effective time". We
conclude that aging and non linear response are dual manifestations of a single
out-of-equilibrium state, which might be a generic situation.
