Multidimensional renewal theory in the non-centered case. Application to   strongly ergodic Markov chains
  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. 
Denis Guibourg (IRMAR), Lo\"ic Herv\'e (IRMAR)
math.PR