empirical distributions {#Sec:empirical}
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Let us consider, as paradigm of the PDFs with two-fold power-law behavior, Eqs. (\[A\]) and (\[B\]), that have a simple exact expression. Actually they have the same functional form, via redefinition of parameters ($\theta,\gamma_\alpha,\gamma_\mu$). This expression has been recently proposed in the literature as an ansatz for fitting the distribution of high-frequency stock-volumes [@vol1], under the form $$\label{fitting} 
\rho(x) = 
\rho_o \frac{(x/x_o)^\nu}
{[1+(q-1)x/x_o]^\frac{1}{q-1} }  \; ,$$ where, in that specific application, $x$ is identified with normalized stock volume. Therefore, identification of the process for real volumes with one of the models above, may allow an econophysical interpretation of the fitting parameters. Table I presents the correspondence between the parameters of Eq. (\[fitting\]) and those of processes [**A**]{} and [**B**]{}, given by Eqs. (\[A\]) and (\[B\]), respectively.

  ------------------- ------------------------------------ ------------------------------------
                                   [**A**]{}                            [**B**]{}
   Eq. (\[fitting\])              Eq. (\[A\])                          Eq. (\[B\])
   \[3mm\] $1/(q-1)$   $1+\gamma_\alpha\theta+\gamma_\mu$   $1+\gamma_\alpha+\gamma_\mu\theta$
     \[3mm\] $\nu$           $\gamma_\alpha\theta$                 $1+\gamma_\mu\theta$
     \[3mm\] $x_o$      $(q-1)\gamma_\mu/\gamma_\alpha$      $(q-1) \gamma_\alpha/\gamma_\mu$
        \[3mm\]                                            
  ------------------- ------------------------------------ ------------------------------------

  : Correspondence amongst model parameters.[]{data-label="table"}

Recall that $\gamma_\alpha\equiv\gamma/\alpha^2$ and $\gamma_\mu\equiv\gamma/\mu^2$ ($\lambda^2\equiv\gamma_\alpha/\gamma_\mu$), thus, the power-law exponent for small values of $x$, given by $\nu$ (see Table), increases with $\gamma$ and $\theta$, and is reduced by either one of the two noise amplitudes: the 