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 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 .