  The Fluctuation Relation for a stationary state, kept at constant energy by a
deterministic thermostat - the Gallavotti-Cohen Theorem -- relies on the
ergodic properties of the system considered. We show that when perturbed by an
energy-conserving random noise, the relation follows trivially for any system
at finite noise amplitude. The time needed to achieve stationarity may stay
finite as the noise tends to zero, or it may diverge. In the former case the
Gallavotti-Cohen result is recovered, while in the latter case, the crossover
time may be computed from the action of `instanton' orbits that bridge
attractors and repellors. We suggest that the `Chaotic Hypothesis' of
Gallavotti can thus be reformulated as a matter of stochastic stability of the
measure in trajectory space. In this form this hypothesis may be directly
tested.
