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Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains

Published online by Cambridge University Press:  15 May 2003

Jean-Pierre Conze
Affiliation:
IRMAR, Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France; conze@univ-rennes1.fr.
Albert Raugi
Affiliation:
IRMAR, Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France; conze@univ-rennes1.fr.
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Abstract

We present a spectral theory for a class of operators satisfying a weak “Doeblin–Fortet" condition and apply it to a class of transition operators. This gives the convergence of the series ∑k≥0krPkƒ, $r \in \mathbb{N}$, under some regularity assumptions and implies the central limit theorem with a rate in $n^{- \frac{1}{2} }$ for the corresponding Markov chain. An application to a non uniformly hyperbolic transformation on the interval is also given.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2003

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