The Nagaev-Guivarc'h method via the Keller-Liverani theorem

La methode de Nagaev-Guivarc'h, via le theoreme de perturbation de Keller et Liverani, a ete appliquee recemment en vu d'etablir des theoremes limites pour des fonctionnelles non bornees de chaines de Markov fortement ergodiques. La difficulte principale dans cette approche est de demontrer des developpements de Taylor pour la valeur propre perturbee de l'operateur de Fourier. Dans ce travail, nous donnons une presentation generale de cette methode, et nous l'etendons en demontrant un theoreme limite local multidimensionnel, un theoreme de Berry-Esseen unidimensionnel, un developpement d'Edgeworth d'ordre 1, et enfin un theoreme de Berry-Esseen multidimensionnel au sens de la distance de Prohorov. Nos applications concernent les chaines de Markov L 2 -fortement ergodiques, υ-geometriquement ergodiques, et les modeles iteratifs. Pour ces exemples, les trois premiers theoremes limites cites precedemment sont satisfaits sous des conditions de moment dont l'ordre est le meme (parfois a e > 0 pres) que dans le cas independant.

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