  We examine a model for the observed temporal variability of powerful blazars
in the $\gamma$-ray band in which the dynamics is described in terms of a
stochastic differential equation, including the contribution of a deterministic
drift and a stochastic term. The form of the equation is motivated by the
current astrophysical framework, accepting that jets are powered through the
extraction of the rotational energy of the central supermassive black hole
mediated by magnetic fields supported by a so-called \emph{magnetically
arrested} accretion disk. We apply the model to the $\gamma$-ray light curves
of several bright blazars and we infer the parameters suitable to describe
them. In particular, we examine the differential distribution of fluxes
($dN/dF_{\gamma}$) and we show that the predicted probability density function
for the assumed stochastic equation naturally reproduces the observed power law
shape at large fluxes $dN/dF_{\gamma} \propto F_{\gamma}^{-\alpha}$ with
$\alpha>2$.
