  Starting from the kinetic equations for the fluctuations and correlations of
a dilute gas of inelastic hard spheres or disks, a Boltzmann-Langevin equation
for the one-particle distribution function of the homogeneous cooling state is
constructed. This equation is the linear Boltzmann equation with a fluctuating
white noise term. Balance equations for the fluctuating hydrodynamic fields are
derived. New fluctuating forces appear as compared with the elastic limit. The
particular case of the transverse velocity field is investigated in detail. Its
fluctuations can be described by means of a Langevin equation, but exhibiting
two main differences with the Landau-Lifshitz theory: the noise is not white,
and its second moment is not determined by the shear viscosity. This shows that
the fluctuation-dissipation relations for molecular fluids do not
straightforwardly carry over to inelastic gases. The theoretical predictions
are shown to be in good agreement with molecular dynamics simulation results.
