  We consider random walks in random Dirichlet environment (RWDE) which is a
special type of random walks in random environment where the exit probabilities
at each site are i.i.d. Dirichlet random variables. On $\Z^d$, RWDE are
parameterized by a $2d$-uplet of positive reals. We prove that for all values
of the parameters, RWDE are transient in dimension $d\ge 3$. We also prove that
the Green function has some finite moments and we characterize the finite
moments. Our result is more general and applies for example to finitely
generated symmetric transient Cayley graphs. In terms of reinforced random
walks it implies that directed edge reinforced random walks are transient for
$d\ge 3$.
