Global Central Limit Theorems for Stationary Markov Chains

Let P be a Markov operator on a general state space ( S , Σ) with an invariant probability measure m , assumed to be ergodic. We study conditions which yield that for every centered non-zero f ∈ L 2 ( m ) a non-degenerate annealed CLT and an L 2 -normalized CLT hold.