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References

  • Bremaud, P. (1999). Markov Chains: Gibbs Fields, Monte Carlo Simulation and Queue, Springer, New York.

    Google Scholar 

  • Diaconis, P. and Stroock, D. (1991). Geometric bounds for eigenvalues of Markov chains, Ann. Appl. Prob., 1(1), 36–61.

    Article  MATH  MathSciNet  Google Scholar 

  • Dobrushin, R. (1956a). Central limit theorems for non-stationary Markov chains, I, Teor. Veroyatnost Primerien, 1, 72–89.

    MathSciNet  Google Scholar 

  • Dobrushin, R. (1956b). Central limit theorems for non-stationary Markov chains, II, Teor. Veroyatnost Primerien, 1, 365–425.

    Google Scholar 

  • Doeblin, W. (1938). Sur deus problemes de M. Kolmogoroff concernant les chaines denombrables, Bull. Soc. Math. France, 52, 210–220.

    MathSciNet  Google Scholar 

  • Doob, J.L. (1953). Stochastic Processes, John Wiley, New York.

    MATH  Google Scholar 

  • Fill, J. (1991). Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, Ann. Appl. Prob., 1(1), 62–87.

    Article  MATH  MathSciNet  Google Scholar 

  • Gudynas, P. (1991). Refinements of the central limit theorem for homogeneous Markov chains, in Limit Theorems of Probability Theory, N.M. Ostianu (ed.), Akad. Nauk SSSR, Moscow, 200–218.

    Google Scholar 

  • Isaacson, D. (1976). Markov Chains:Theory and Applications, John Wiley, New York.

    MATH  Google Scholar 

  • Jones, G. (2004). On the Markov chain central limit theorem, Prob. Surveys, 1, 299–320.

    Google Scholar 

  • Maxwell, M. and Woodroofe, M. (2000). Central limit theorems for additive functionals of Markov chains, Ann. Prob., 28(2), 713–724.

    Article  MATH  MathSciNet  Google Scholar 

  • Meyn, S.P. and Tweedie, R.L. (1993). Markov Chains and Stochastic Stability, Springer, New York.

    MATH  Google Scholar 

  • Nagaev, S. (1957). Some limit theorems for stationary Markov chains, Teor. Veroyat-nost Primerien, 2, 389–416.

    MathSciNet  Google Scholar 

  • Norris, J.R. (1997). Markov Chains, Cambridge University Press, Cambridge.

    MATH  Google Scholar 

  • Roberts, G.O. and Rosenthal, J.S. (1997). Geometric ergodicity and hybrid Markov chains, Electron. Commun. Prob., 2, 13–25.

    MATH  MathSciNet  Google Scholar 

  • Rosenblatt, M. (1971). Markov Processes, Structure, and Asymptotic Behavior, Springer, New York.

    MATH  Google Scholar 

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DasGupta, A. (2008). Central Limit Theorem for Markov Chains. In: Asymptotic Theory of Statistics and Probability. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-75971-5_10

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