Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains
IRMAR, Université de Rennes I,
Campus de Beaulieu, 35042 Rennes Cedex, France; email@example.com.
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, , 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.
Mathematics Subject Classification: 60J10 / 37A05 / 37A25
Key words: Transfer operator / convergence of iterates / Markov chains / rate in the TCL for dynamical systems / Borel-Cantelli property / non uniformly hyperbolic map.
© EDP Sciences, SMAI, 2003