  Dynamics of deterministic systems perturbed by random additive noise is
characterized quantitatively. Since for such systems the KS-entropy diverges we
analyse the difference between the total entropy of a noisy system and the
entropy of the noise itself. We show that this quantity is non negative and in
the weak noise limit is conjectured to tend to the KS-entropy of the
deterministic system. In particular, we consider one-dimensional systems with
noise described by a finite-dimensional kernel, for which the Frobenius-Perron
operator can be represented by a finite matrix.
