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| HAL : hal-00632893, version 2 |
| arXiv : 1110.3603 |
| DOI : 10.1007/s11118-012-9282-0 |
| Fiche détaillée |  Récupérer au format |
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| Potential Analysis 38, 2 (2013) 471-497 |
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| Versions disponibles : | v1 (17-10-2011) | v2 (10-01-2012) |
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| Multidimensional renewal theory in the non-centered case. Application to strongly ergodic Markov chains. |
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| Denis Guibourg 1Loïc Hervé 1 |
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| (2013) |
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| 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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| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Théorie ergodique |
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| Domaine | : | Mathématiques/Probabilités |
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| Fourier techniques – spectral method |
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| hal-00632893, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00632893 | |
| oai:hal.archives-ouvertes.fr:hal-00632893 | |
| Contributeur : Loïc Hervé | |
| Soumis le : Mardi 10 Janvier 2012, 12:29:55 | |
| Dernière modification le : Lundi 18 Mars 2013, 10:02:55 | |
