  We present a stochastic model based on the Monte Carlo technique to study the
inhomogeneous chemical evolution of the Galactic halo. In particular, we
consider the local enrichment and subsequent mixing of the interstellar gas
resulting from bursts of star formation, following explicitly the fragmentation
and coalescence of interstellar gas clouds. The model takes into account the
mixing of halo gas through cloud-cloud collisions and the delayed mixing of
supernova ejecta into the interstellar medium. The consequences of the infall
of halo gas onto the Galactic disk are also discussed. The mass spectrum of
clouds, the age-metallicity relation, and the G-dwarf distribution are
investigated at different times. We analyze in detail the predictions of our
model for the abundance of elements like Eu, Ba, and Sr in the Galactic halo,
following their production by $r$-process nucleosynthesis for different
assumptions on the supernova mass range. Finally, we compare our results with
spectroscopic data for the chemical composition of metal-poor halo stars.
