The Central Limit Theorem for Markov Chains with General State Space

We consider a Markov chain with general state space and an embedded Markov chain sampled at the times of successive returns to a subsetA₀ of the state space.We assume that the latter chain is uniformly ergodic but the originalMarkov chain need not possess this property.We develop amodification of the spectralmethod and utilize it in proving the central limit theorem for theMarkov chain under consideration.