On the central limit theorem for geometrically ergodic Markov chains

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Batch means and spectral variance estimators in Markov chain Monte Carlo (2008, background): “where τi, i = 1, 2 are the first two times at which regenerations occur in the split-chain; see Hobert et al. (2002), Jones and Hobert (2001) and Mykland et al.”
On the Markov chain central limit theorem (2004, background): “tions. See [ 24 ] for a construction that establishes the existence of a geometrically ergodic Markov chain and a function f such that E f 2(x) <1 yet a CLT fails for any choice of 2. Also, see [2] for a counterexample with the same conclusion.”
Stationarity and geometric ergodicity of BEKK multivariate GARCH models (2011, unknown): “4 (see [19] and also [20, 22]).”
General state space Markov chains and MCMC algorithms (2004, background): “However, it was recently solved by Häggström [36], who produced a counter-example to prove the following: Theorem 26.”
Geometric ergodicity and the spectral gap of non-reversible Markov chains (2009, methodology): “Based on earlier counterexamples constructed by Häggström [9, 10] and Bradley [1], in Section 3 we prove the following: Theorem 1.”