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

2011/10/17 by Denis Guibourg, Guibourg, Denis, Loı̈c Hervé +1
Decision Sciences · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1110.3603

openalex publication_date 2011/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (S_n)_n be a R^d-valued random walk (d≥2). 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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