  In hybrid inflation models, typically only a tiny fraction of possible
initial conditions give rise to successful inflation, even if one assumes
spatial homogeneity. We analyze some possible solutions to this initial
conditions problem, namely assisted hybrid inflation and hybrid inflation on
the brane. While the former is successful in achieving the onset of inflation
for a wide range of initial conditions, it lacks sound physical motivation at
present. On the other hand, in the context of the presently much discussed
brane cosmology, extra friction terms appear in the Friedmann equation which
solve this initial conditions problem in a natural way.
