A regeneration proof of the central limit theorem for uniformly ergodic Markov chains

Ajay Jasra and Chao Yang

Statistics & Probability Letters, 2008, vol. 78, issue 12, 1649-1655

Abstract: Let (Xn) be a Markov chain on measurable space with unique stationary distribution [pi]. Let be a measurable function with finite stationary mean . Ibragimov and Linnik [Ibragimov, I.A., Linnik, Y.V., 1971. Independent and Stationary Sequences of Random Variables. Wolter-Noordhoff, Groiningen] proved that if (Xn) is geometrically ergodic, then a central limit theorem (CLT) holds for h whenever [pi](h2+[delta]) 0. Cogburn [Cogburn, R., 1972. The central limit theorem for Markov processes. In: Le Cam, L.E., Neyman, J., Scott, E.L. (Eds.), Proc. Sixth Ann. Berkley Symp. Math. Statist. and Prob., 2. pp. 485-512] proved that if a Markov chain is uniformly ergodic, with [pi](h2)

Date: 2008
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