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Global central limit theorems for Markov chains

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  • Cuny, Christophe
  • Lin, Michael

Abstract

Let P be a Markov operator on a general state space (S,Σ) with invariant probability m, assumed ergodic. We study conditions which yield that for every centered 0≠f∈L2(m) a non-degenerate annealed CLT and an L2-normalized CLT hold.

Suggested Citation

  • Cuny, Christophe & Lin, Michael, 2025. "Global central limit theorems for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:spapps:v:190:y:2025:i:c:s0304414925001504
    DOI: 10.1016/j.spa.2025.104709
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    References listed on IDEAS

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    1. Esseen, Carl-Gustav & Janson, Svante, 1985. "On moment conditions for normed sums of independent variables and martingale differences," Stochastic Processes and their Applications, Elsevier, vol. 19(1), pages 173-182, February.
    2. El Machkouri, Mohamed & Jakubowski, Adam & Volný, Dalibor, 2020. "Stable limits for Markov chains via the Principle of Conditioning," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1853-1878.
    3. Peligrad, Magda, 2020. "A new CLT for additive functionals of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5695-5708.
    4. Richard C. Bradley, 2021. "On some basic features of strictly stationary, reversible Markov chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 499-533, September.
    5. Dalibor Volný, 2010. "Martingale Approximation and Optimality of Some Conditions for the Central Limit Theorem," Journal of Theoretical Probability, Springer, vol. 23(3), pages 888-903, September.
    6. Richard C. Bradley, 1997. "On Quantiles and the Central Limit Question for Strongly Mixing Sequences," Journal of Theoretical Probability, Springer, vol. 10(2), pages 507-555, April.
    Full references (including those not matched with items on IDEAS)

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