Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains
ESAIM: Probability and Statistics, Volume 7 (2003), p. 115-146

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 k0 k r P k f, r, 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.

DOI : https://doi.org/10.1051/ps:2003003
Classification:  60J10,  37A05,  37A25
Keywords: transfer operator, convergence of iterates, Markov chains, rate in the TCL for dynamical systems, Borel-Cantelli property, non uniformly hyperbolic map
@article{PS_2003__7__115_0,
     author = {Conze, Jean-Pierre and Raugi, Albert},
     title = {Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains},
     journal = {ESAIM: Probability and Statistics},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2003},
     pages = {115-146},
     doi = {10.1051/ps:2003003},
     zbl = {1018.60072},
     mrnumber = {1956075},
     language = {en},
     url = {http://www.numdam.org/item/PS_2003__7__115_0}
}
Conze, Jean-Pierre; Raugi, Albert. Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains. ESAIM: Probability and Statistics, Volume 7 (2003) pp. 115-146. doi : 10.1051/ps:2003003. http://www.numdam.org/item/PS_2003__7__115_0/

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