  The dynamics of a tracer particle in a stationary driven granular gas is
investigated. We show how to transform the linear Boltzmann equation describing
the dynamics of the tracer into a master equation for a continuous Markov
process. The transition rates depend upon the stationary velocity distribution
of the gas. When the gas has a Gaussian velocity probability distribution
function (pdf), the stationary velocity pdf of the tracer is Gaussian with a
lower temperature and satisfies detailed balance for any value of the
restitution coefficient $\alpha$. As soon as the velocity pdf of the gas
departs from the Gaussian form, detailed balance is violated. This
non-equilibrium state can be characterized in terms of a Lebowitz-Spohn action
functional $W(\tau)$ defined over trajectories of time duration $\tau$. We
discuss the properties of this functional and of a similar functional
$\bar{W}(\tau)$ which differs from the first for a term which is non-extensive
in time. On the one hand we show that in numerical experiments, i.e. at finite
times $\tau$, the two functionals have different fluctuations and $\bar{W}$
always satisfies an Evans-Searles-like symmetry. On the other hand we cannot
observe the verification of the Lebowitz-Spohn-Gallavotti-Cohen (LS-GC)
relation, which is expected for $W(\tau)$ at very large times $\tau$. We give
an argument for the possible failure of the LS-GC relation in this situation.
We also suggest practical recipes for measuring $W(\tau)$ and $\bar{W}(\tau)$
in experiments.
