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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,
,
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.
We study the convergence to equilibrium of n-samples of independent Markov
chains in discrete and continuous time. They are defined as Markov chains on
the n-fold Cartesian product of the initial state space by itself, and they
converge to the direct product of n copies of the initial stationary
distribution. Sharp estimates for the convergence speed are given in
terms of the spectrum of the initial chain. A cutoff phenomenon occurs in the
sense that as n tends to infinity, the total variation...
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