  We investigate the effect of white-noise perturbations on chaotic
trajectories in open billiards. We focus on the temporal decay of the survival
probability for generic mixed-phase-space billiards. The survival probability
has a total of five different decay regimes that prevail for different
intermediate times. We combine new calculations and recent results on noise
perturbed Hamiltonian systems to characterize the origin of these regimes, and
to compute how the parameters scale with noise intensity and billiard openness.
Numerical simulations in the annular billiard support and illustrate our
results.
