1 results
Convergence of iterates of a transfer operator,application to dynamical systems and to Markov chains
-
- Journal:
- ESAIM: Probability and Statistics / Volume 7 / March 2003
- Published online by Cambridge University Press:
- 15 May 2003, pp. 115-146
- Print publication:
- March 2003
-
- Article
- Export citation
-
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 theoremwith 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.
