mean reversion present strong correlations that prevent convergence to either Gauss or Lévy limits[@multi3] and lead to $q$-Gaussian distributions. This suggests that similar correlations may persist in mean-reverting processes with the additive-multiplicative character. Once Eq. (\[ILE\]) leads to PDFs in such a good agreement with empirical ones, it is worth performing a detailed study and comparison of real and artificial time series to test the models with respect to the dynamics. Elucidating this point deserves a careful separate treatment.

[**Acknowledgments:** ]{} We are grateful to S. Miccichè, G. Bonanno, F. Lillo and R.N. Mantegna for communicating their numerical data in Ref. [@micciche].

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