  During solar flares a large amount of electrons are accelerated within the
plasma present in the solar atmosphere. Accurate measurements of the motion of
these electrons start becoming available from the analysis of hard X-ray
imaging-spectroscopy observations. In this paper, we discuss the linearized
perturbations of the Boltzmann kinetic equation describing an ensemble of
electrons accelerated by the energy release occurring during solar flares.
Either in the limit of high energy or at vanishing background temperature such
an equation reduces to a continuity equation equipped with an extra force of
stochastic nature. This stochastic force is actually described by the well
known energy loss rate due to Coulomb collision with ambient particles, but, in
order to match the collision kernel in the linearized Boltzmann equation it
needs to be treated in a very specific manner. In the second part of the paper
the derived continuity equation is solved with some hyperbolic techniques, and
the obtained solution is written in a form suitable to be compared with data
gathered by hard X-ray imaging-spectroscopy telescopes. Finally, a first
validation of the model with NASA Reuven Ramaty High Energy Solar Spectroscopic
Imager spectrometer measurements is provided.
