HAL: hal-00632893, version 2

arXiv: 1110.3603

DOI: 10.1007/s11118-012-9282-0

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Potential Analysis 38, 2 (2013) 471-497

Available versions:

v1 (2011-10-17)

v2 (2012-01-10)

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

Denis Guibourg 1, Loïc Hervé 1

(2013)

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.

1:	Institut de Recherche Mathématique de Rennes (IRMAR)
	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

Research team: Théorie ergodique

Subject

:

Mathematics/Probability

Keyword(s): Fourier techniques – spectral method

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From: Loïc Hervé <>

Submitted on: Tuesday, 10 January 2012 12:29:55

Updated on: Monday, 18 March 2013 10:02:55