general class of stochastic differential equations given by $$\label{ILE0}
{\rm d} x \;=\;-\gamma[x-\theta]x^{r-1}{\rm d}t + \mu x^s{\rm d}w \;,$$ where, $\theta, \gamma,\mu>0$, $r,s\in\mathbb{R}$, and $w$ is a Wiener process, such that $\langle {\rm d}w\rangle=0$ and $\langle ({\rm d}w)^2\rangle=2{\rm d}t$. The definition of the stochastic process is completed by the Itô prescription. This class generalizes well-known models employed to describe the dynamics of mean-reverting financial variables[@juros]. In particular, some traditional processes for modeling volatilities or, mainly, squared volatilities are the Hull-White ($r=1,s=1$)[@hw] and the Heston ($r=1,s=1/2$)[@heston] models, the latter also known either as Cox-Ingersoll-Ross[@cir] or Feller process[@feller]. The arithmetic ($r=1,s=0$) and geometric ($r=2,s=1$) Ornstein-Ulhenbeck processes are particular cases too. Moreover, several other models employed in the literature of volatilities are related to this class[@others; @micciche].

Different values of $r$ in Eq. (\[ILE0\]) represent different possible relaxation mechanisms of amplitude $\gamma$, determined, amongst other factors, by constraints, flux of information, stock liquidity and risk aversion, which are particular of a given market. Notice that the restoring force in Eq. (\[ILE0\]) corresponds to a confining potential, with minimum at $\theta$, for all $r\in\mathbb{R}$. The larger $r$, the more attractive the potential for large $x$, but the less attractive for vanishing $x$. Similarly, different 