  In this paper we consider the variability of the luminosity of a compact
object (CO) powered by the accretion of an extremely inhomogeneous ("clumpy")
stream of matter. The accretion of a single clump results in an X-ray flare: we
adopt a simple model for the response of the CO to the accretion of a single
clump, and derive a stochastic differential equation (SDE) for the accretion
powered luminosity $L(t)$. We put the SDE in the equivalent form of an equation
for the flares' luminosity distribution (FLD), and discuss its solution in the
stationary case. As a case study, we apply our formalism to the analysis of the
FLDs of Super-Giant Fast X-ray Transients (SFXTs), a peculiar sub-class of High
Mass X-ray Binary Systems (HMXBs). We compare our theoretical FLDs to the
distributions observed in the SFXTs IGR J16479-4514, IGR J17544-2619 and XTE
J1739-302. Despite its simplicity, our model fairly agrees with the observed
distributions, and allows to predict some properties of the stellar wind.
Finally, we discuss how our model may explain the difference between the broad
FLD of SFXTs and the much narrower distribution of persistent HMXBs.
