the market and the informational coupling among the traders, respectively. On the other hand, power-law exponents and coefficients of exponential-like functions depend also on the reduced parameters $\gamma_\mu$, $\gamma_\alpha$ and on $\theta$. This means that one may expect universal behavior among markets that share similar rules (same $r$ and $s$) and same rescaled restoring parameters, for a properly normalized reference level $\theta$. Summarizing, the additive-multiplicative processes given by Eq. (\[ILE\]) provide a general realistic framework to describe the shape of empirical distributions for financial, as well as, for physical systems. An illustrative application to empirical volatility data was presented in Sect. \[Sec:empirical\], showing excellent results.

The statistical description of a market should include its dynamical properties such as the temporal decay of correlations. In real time series of volatilities[@liu] and volumes[@volumes], power-law decaying correlations have been observed. It is worth noting that stochastic processes with additive-multiplicative structure (without mean reversion) are being currently studied in connection with a generalization of standard (Boltzmann-Gibbs) statistical mechanics, recently proposed by C. Tsallis [@tsallis]. The PDFs associated to this new formalism generalize the exponential weights, namely, $\exp_q(-x) \equiv (1-[1-q]x)^\frac{1}{1-q}$ \[entering as a factor in Eq. (\[fitting\])\]. The time series arising from additive-multiplicative processes without 