A regeneration proof of the central limit theorem for uniformly ergodic Markov chains
نویسندگان
چکیده
E h(x)π(dx). Ibragimov and Linnik (1971) proved that if (Xn) is geometrically ergodic, then a central limit theorem (CLT) holds for h whenever π(|h|) < ∞, δ > 0. Cogburn (1972) proved that if a Markov chain is uniformly ergodic, with π(h) < ∞ then a CLT holds for h. The first result was re-proved in Roberts and Rosenthal (2004) using a regeneration approach; thus removing many of the technicalities of the original proof. This raised an open problem: to provide a proof of the second result using a regeneration approach. In this paper we provide a solution to this problem.
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