  The unpredictability in chaotic scattering problems is a fundamental topic in
physics that has been studied either in purely conservative systems or in the
presence of weak perturbations. In many systems noise plays an important role
in the dynamical behavior and it models their internal irregularities or their
coupling with the environment. In these situations the unpredictability is
affected by both the chaotic dynamics and the stochastic fluctuations. In the
presence of noise two trajectories with the same initial condition can evolve
in different ways and converge to a different asymptotic behavior. For this
reason, even the exact knowledge of the initial conditions does not necessarily
lead to the predictability of the final state of the system. Hence, the noise
can be considered as an important source of unpredictability that cannot be
fully understood using the conventional methods of nonlinear dynamics, such as
the exit basins and the uncertainty exponent. By adopting a probabilistic point
of view, we develop the concepts of probability basin, uncertainty basin and
noise-sensitivity exponent, that allow us to carry out both a quantitative and
qualitative analysis of the unpredictability on noisy chaotic scattering
problems.
