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Uniform CLT for Markov chains with a countable state space

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  • Levental, Shlomo

Abstract

For an irreducible Markov chain taking integer values which has a finite second moment for the first return time from some integer to itself, we find a necessary and sufficient condition for a CLT which is uniform over all subsets of the integers. This is a generalization of one of the results in Durst and Dudley (1981) who worked in the i.i.d. case. An example that clarifies the difference between the i.i.d. case and Markov case is presented.

Suggested Citation

  • Levental, Shlomo, 1990. "Uniform CLT for Markov chains with a countable state space," Stochastic Processes and their Applications, Elsevier, vol. 34(2), pages 245-253, April.
    • Handle: RePEc:eee:spapps:v:34:y:1990:i:2:p:245-253
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    Cited by:

    1. Tsai, Tsung-Hsi, 2001. "The CLT for Markov chains with a countable state space embedded in the space lp," Stochastic Processes and their Applications, Elsevier, vol. 91(1), pages 39-46, January.
    2. Tsai, Tsung-Hsi, 2000. "Empirical law of the iterated logarithm for Markov chains with a countable state space," Stochastic Processes and their Applications, Elsevier, vol. 89(2), pages 175-191, October.
    3. Djellout, H. & Guillin, A., 2001. "Moderate deviations for Markov chains with atom," Stochastic Processes and their Applications, Elsevier, vol. 95(2), pages 203-217, October.

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