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

Denis Guibourg (1) , Loïc Hervé (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Fourier techniques; spectral method

Domaines: Probabilités [math.PR]

Denis Guibourg, Loïc Hervé. Multidimensional renewal theory in the non-centered case. Application to strongly ergodic Markov chains.. Potential Analysis, 2013, 38 (2), pp.471-497. ⟨10.1007/s11118-012-9282-0⟩. ⟨hal-00632893v2⟩