Abstract
The aim of this paper is to prove a central limit theorem and an invariance principle for an additive functional of an ergodic Markov chain on a general state space, with respect to the law of the chain started at a point. No irreducibility assumption nor mixing conditions are imposed; the only assumption bears on the growth of the L 2 -norms of the ergodic sums for the function generating the additive functional, which must be with . The result holds almost surely with respect to the invariant probability of the chain.
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