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arXiv · 1110.3603

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

Denis Guibourg·Loïc Hervé
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Abstract

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.

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Denis Guibourg, Loïc Hervé. 2011-10-17. Multidimensional renewal theory in the non-centered case. Application to strongly ergodic Markov chains. https://arxiv.org/abs/1110.3603

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