Abstract
In this paper we consider stationary Markov chains with trivial two-sided tail sigma field, and prove that additive functionals satisfy the central limit theorem provided the variance of partial sums divided by n is bounded.
Funding Statement
Supported by the NSF grant DMS-2054598.
Acknowledgments
The author would like to thank Yizao Wang, Richard Bradley and Michael Lin for useful discussions. Many thanks for the referee’s valuable comments and his/her time spent in reviewing the paper.
Citation
Magda Peligrad. "On the CLT for stationary Markov chains with trivial tail sigma field." Electron. Commun. Probab. 28 1 - 7, 2023. https://doi.org/10.1214/23-ECP509
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