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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 theorem
with 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.
