Self-generated power-law tails in probability distributions

We consider random processes characterized by the presence of correlations in their variance, or more generally in some of their moments. Typical examples are constituted by autoregressive conditional heteroskedasticity (ARCH) processes which are known to display power-law tails in the associated probability distributions. Here, we determine the corresponding exponents exactly and extend these results to relaxation phenomena which can be expected to play a role in natural sciences.