  We obtain two-sided bounds for the density of stochastic processes satisfying
a weak H\"ormander condition. In particular we consider the cases when the
support of the density is not the whole space and when the density has various
asymptotic regimes depending on the starting/final points considered (which are
as well related to the number of brackets needed to span the space in
H\"ormander's theorem). The proofs of our lower bounds are based on Harnack
inequalities for positive solutions of PDEs whereas the upper bounds derive
from the probabilistic representation of the density given by the Malliavin
calculus.
