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Let $(S_n)_n$ be a $R^d$-valued random walk ($d\geq2$). Using Babillot'smethod [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 oneobtained for random walks with i.i.d. non-centered increments. This statementis applied to additive functionals of strongly ergodic Markov chains under thenon-lattice condition and (almost) optimal moment conditions.

Multidimensional renewal theory in the non-centered case. Application to strongly ergodic Markov chains