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 , , under some regularity assumptions and implies the central limit theorem with a rate in for the corresponding Markov chain. An application to a non uniformly hyperbolic transformation on the interval is also given.
Mots clés : 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}, pages = {115--146}, publisher = {EDP-Sciences}, volume = {7}, year = {2003}, doi = {10.1051/ps:2003003}, mrnumber = {1956075}, zbl = {1018.60072}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps:2003003/} }
TY - JOUR AU - Conze, Jean-Pierre AU - Raugi, Albert TI - Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains JO - ESAIM: Probability and Statistics PY - 2003 SP - 115 EP - 146 VL - 7 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps:2003003/ DO - 10.1051/ps:2003003 LA - en ID - PS_2003__7__115_0 ER -
%0 Journal Article %A Conze, Jean-Pierre %A Raugi, Albert %T Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains %J ESAIM: Probability and Statistics %D 2003 %P 115-146 %V 7 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps:2003003/ %R 10.1051/ps:2003003 %G en %F 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, Tome 7 (2003), pp. 115-146. doi : 10.1051/ps:2003003. http://archive.numdam.org/articles/10.1051/ps:2003003/
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