References
- J. Aaronson, M. Lin, and B. Weiss, Mixing properties of Markov operators and ergodic transformations, and ergodicity of Cartesian products, Israel J. Math. 33 (1979), no. 3–4, 198–224.
- M.E. Becker, A condition equivalent to uniform ergodicity, Studia Math. 167 (2005), no. 3, 215–218.
- R.C. Bradley, Information regularity and the central limit question, Rocky Mountain J. Math. 13 (1983), no. 1, 77–97.
- R.C. Bradley, Basic properties of strong mixing conditions. A survey and some open questions, Probab. Surv. 2 (2005), 107–144.
- R.C. Bradley, On some basic features of strictly stationary, reversible Markov chains, J. Time Series Anal. 42 (2021), no. 5–6, 499–533.
- R.C. Bradley, On some possible combinations of mixing rates for strictly stationary, reversible Markov chains, Rocky Mountain J. Math. 54 (2024), no. 2, 387–406.
- F.E. Browder, On the iteration of transformations in noncompact minimal dynamical systems, Proc. Amer. Math. Soc. 9 (1958), 773–780.
- Y.S. Chow and H. Teicher, Probability Theory. Independence, Interchangeability, Martingales, Second Ed., Springer Texts Statist., Springer-Verlag, New York-Berlin, 1988.
- Yu.A. Davydov, On the strong mixing property for Markov chains with a countable number of states, Soviet Math. Dokl. 10 (1969), 825–827.
- Yu.A. Davydov, Mixing conditions for Markov chains, Theory Probab. Appl. 18 (1973), no. 2, 312–328.
- Y. Derriennic and M. Lin, Variance bounding Markov chains, L2-uniform mean ergodicity and the CLT, Stoch. Dyn. 11 (2011), no. 1, 81–94.
- P. Doukhan, P. Massart, and E. Rio, The functional central limit theorem for strongly mixing processes, Ann. Inst. H. Poincaré Probab. Statist. 30 (1994), no. 1, 63–82.
- S.R. Foguel, Powers of a contraction in Hilbert space, Pacific J. Math. 13 (1963), 551–562.
- J. Glück, Spectral gaps for hyperbounded operators, Adv. Math. 362 (2020), 106958, 24 pp.
- M.I. Gordin and B.A. Lifshits, The central limit theorem for stationary Markov processes, Soviet Math. Dokl. 19 (1978), 392–394.
- O. Häggström, On the central limit theorem for geometrically ergodic Markov chains, Probab. Theory Related Fields 132 (2005), no. 1, 74–82. Acknowledgement of priority in: Probab. Theory Related Fields 135 (2006), no. 3, 470.
- L. Hervé and F. Pène, The Nagaev-Guivarc’h method via the Keller-Liverani theorem, Bull. Soc. Math. France 138 (2010), no. 3, 415–489.
- I.A. Ibragimov, Some limit theorems for stationary processes, Theory Probab. Appl. 7 (1962), no. 4, 349–382.
- I.A. Ibragimov and Yu.V. Linnik, Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff Publishing, Groningen, 1971.
- M. Lin, On the uniform ergodic theorem, Proc. Amer. Math. Soc. 43 (1974), 337–340.
- S.V. Nagaev, More exact limit theorems for homogeneous Markov chains, Theory Probab. Appl. 6 (1961), no. 1, 62–81.
- G.O. Roberts and J.S. Rosenthal, Geometric ergodicity and hybrid Markov chains, Electron. Comm. Probab. 2 (1997), no. 2, 13–25.
- G.O. Roberts and R.L. Tweedie, Geometric L2 and L1 convergence are equivalent for reversible Markov chains, J. Appl. Probab. 38A (2001), 37–41.
- M. Rosenblatt, Markov Processes. Structure and Asymptotic Behavior, Die Grundlehren der mathematischen Wissenschaften, Band 184, Springer-Verlag, New York-Heidelberg, 1971.
- E. Slutsky, Über stochastische Asymptoten und Grenzwerte, Metron 5 (1925), no. 3, 3–89. See lipari.istat.it/digibib/Metron.
- W. Stadje and A. Wübker, Three kinds of geometric convergence for Markov chains and the spectral gap property, Electron. J. Probab. 16 (2011), no. 34, 1001–1019.