A new CLT for additive functionals of Markov chains

Magda Peligrad

Stochastic Processes and their Applications, 2020, vol. 130, issue 9, 5695-5708

Abstract: 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 additive functionals of a stationary and totally ergodic Markov chain with var(Sn)∕n uniformly bounded, satisfies a n−central limit theorem with a random centering. We do not assume that the Markov chain is irreducible and aperiodic. However, the random centering is not needed if the Markov chain satisfies stronger forms of ergodicity. In absence of ergodicity the convergence in distribution still holds, but the limiting distribution might not be normal.

Keywords: Markov chains; Variance of partial sums; Central limit theorem; Projective criteria; Absolute regularity (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2020.04.004

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