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We examine a model for the observed temporal variability of powerful blazarsin the $\gamma$-ray band in which the dynamics is described in terms of astochastic differential equation, including the contribution of a deterministicdrift and a stochastic term. The form of the equation is motivated by thecurrent astrophysical framework, accepting that jets are powered through theextraction of the rotational energy of the central supermassive black holemediated by magnetic fields supported by a so-called \emph{magneticallyarrested} accretion disk. We apply the model to the $\gamma$-ray light curvesof several bright blazars and we infer the parameters suitable to describethem. In particular, we examine the differential distribution of fluxes($dN/dF_{\gamma}$) and we show that the predicted probability density functionfor the assumed stochastic equation naturally reproduces the observed power lawshape at large fluxes $dN/dF_{\gamma} \propto F_{\gamma}^{-\alpha}$ with$\alpha>2$.

On the distribution of fluxes of gamma-ray blazars: hints for a stochastic process?