r-2s$. Symbols correspond to the special processes [**A**]{} \[Eq. (\[A\])\] and [**B**]{} \[Eq. (\[B\])\]. []{data-label="fig:am"}](vfigure2.eps){width="40.00000%"}

In general, the class of asymptotic behavior is ruled by $(s,r)$ that determine the form of market laws. This holds, of course, as soon as the remaining parameters assume moderate values. For instance, the factor $\lambda^2\equiv\gamma_\alpha/\gamma_\mu$ accompanies $x^{2s}$ in the formula for $\rho(x)$ \[Eqs. (\[FPss\])-(\[intmarg\])\], then, extreme values of $\lambda$ will change the asymptotic regime. In fact, in the limit $\alpha=0$ (negligible additive noise, corresponding to $\lambda\to \infty$), different laws arise, as we have seen in the precedent Section.

Summarizing, we have shown the whole picture of asymptotic behaviors that a general class of additive-multiplicative processes produce. As a consequence of the extra additive noise, new types of asymptotic behaviors emerge. Specially interesting solutions arise in the marginal cases $r=0,-1$ where two-fold power-law PDFs are found.

Moreover, additive-multiplicative processes lead to higher richness of crossover behaviors, with respect to purely multiplicative processes. Therefore, the appearance of new PDF shapes exceeds the one resulting from the mere analysis of the asymptotic regimes. This is specially important because depending on the values of the parameters, the true asymptotic regime might fall outside the observable range.

Comparison with 