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Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains. (English) Zbl 1018.60072
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 \(\sum_{k\geq 0}k^rP^kf\), \(r\in\mathbb{N}\), under some regularity assumptions and implies the central limit theorem with a rate in \(n^{-1/2}\) for the corresponding Markov chain. An application to a non uniformly hyperbolic transformation on the interval is also given.

MSC:
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
37A05 Dynamical aspects of measure-preserving transformations
37A25 Ergodicity, mixing, rates of mixing
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