  Let $(S_n)_n$ be a $R^d$-valued random walk ($d\geq2$). Using Babillot's
method [2], we give general conditions on the characteristic function of $S_n$
under which $(S_n)_n$ satisfies the same renewal theorem as the classical one
obtained for random walks with i.i.d. non-centered increments. This statement
is applied to additive functionals of strongly ergodic Markov chains under the
non-lattice condition and (almost) optimal moment conditions.
