We obtain optimal rates in the central limit theorem (CLT) for additive functionals of uniformly elliptic inhomogeneous Markov chains without any assumptions on the growth rates of the variance of the underlying partial sums. (The CLT itself is due to Dobrushin (1956) and it holds in greater generality.)
 
We will also discuss Edgeworth expansions (i.e., the correction terms in the CLT) of order one for general classes of functionals, which provide a structural characterization of having better than optimal CLT rates.
 
Finally, for several classes of additive functionals (e.g., Holder continuous), we will provide optimal conditions for Edgeworth expansions of an arbitrary order.
 
The talk is based on a joint work with Dmitry Dolgopyat.