A new CLT for additive functionals of Markov chains

Magda Peligrad

Published 2019-10-15Version 1

In this paper we study the central limit theorem for additive functionals of stationary Markov chains with general state space by using a new idea involving conditioning with respect to both the past and future of the chain. Practically, we show that any stationary and ergodic Markov chain with the variance of partial sums linear in n, satisfies a central limit theorem with a random centering. We do not assume that the Markov chain is irreducible or aperiodic. However, the random centering is not needed if the Markov chain satisfies stronger forms of ergodicity.