addition to the positivity of $s$, point to model [**A**]{} as a more realistic long-term process.

The fitting parameters in Fig. \[fig:data\] lead to ($\theta,\gamma_\mu,\gamma_\alpha)_{\rm \bf A}\simeq(0.50,2.4,4.4)$ or ($\theta,\gamma_\mu,\gamma_\alpha)_{\rm \bf B}\simeq(0.19,6.3,3.4)$. In both cases, $\gamma_\mu,\gamma_\alpha>1$, as expected for regulated markets. While $\langle v \rangle =1$, because empirical volatility is normalized, $\langle x \rangle =\langle v^2 \rangle \simeq 1.3$ and the mode is $x^{max}\simeq 0.35$, consistently with Eqs. (\[averages\])-(\[maxima\]).

Numerical integration of ILEs (\[ILEA\]) and (\[ILEB\]), by standard methods[@books], shows that both processes produce time series with bursting or clustering effects, as observed in real sequences. However, process [**B**]{} may present, for some values of the parameters, a kind of ergodicity breaking, with large jumps to a state basically governed by additive noise. This occurs because, once $x$ jumps to a high value, both the restoring force and the effective amplitude of multiplicative noise become small as to pull $x$ back to its reference level. Then, relaxation is slowed down and the regime of high volatility persists for long time stretches. Although a process with $s<0$ is not expected to be a realistic model for very long time intervals, it can model, for instance, the transient behavior of the market around 