  We consider a dynamical system which has a stable attractor and which is
perturbed by an additive noise. Under some quite typical conditions, the
fluctuations from the attractor are intermittent and have a probability
distribution with power-law tails. We show that this results from a stochastic
cascade of amplification of fluctuations due to transient periods of
instability. The exponent of the power-law is interpreted as a negative fractal
dimension.
