  We use the framework of sample space reducing processes (SSR) as an
alternative to Boltzmann equation based approaches, to derive the energy and
velocity distribution functions of an inelastic gas in a box as an example for
a dissipative, driven system. SSR processes do not assume molecular chaos and
are characterized by a specific type of eigenvalue equation whose solutions
represent stationary distribution functions. The equations incorporate the
geometry of inelastic collisions and a driving mechanism in a transparent way.
Energy is injected by boosting particles that hit the walls of the container to
high energies. The numerical solution of the resulting equations yields power
laws over the entire energy region. The exponents decrease with the driving
rate from about $2$ to below $1.5$ and depend on the coefficient of
restitution. Results are confirmed with a molecular dynamics simulation in 3D
with the same driving mechanism. We believe that these distribution functions
are observable in experimental situations; the abundance of power laws in
driven dissipative systems might be a sign of the generality of the result.
