Abstract: We obtain optimal rates in the central limit theorem for additive functionals of uniformly elliptic inhomogeneous Markov chains without any assumptions on the growth rates of the variance of the underlying partial sums.
In addition, we will discuss the lattice-obstruction for the Edgeworth expansion of order one for general classes of functionals. The main result states that either the additive functionals are essentially lattice valued or we get better rates by considering an additional correction term to the CLT (in general, this results fails in the lattice case). For several classes of additive functionals (e.g. Holder continuous) we also provide optimal conditions for the Edgeworth expansions of an arbitrary order to hold true.
This is a joint work with Dmitry Dolgopyat (UMD).
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