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Limit theorems for correlated Bernoulli random variables

Author

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  • James, Barry
  • James, Kang
  • Qi, Yongcheng

Abstract

In this paper we study limit theorems for a class of correlated Bernoulli processes. We obtain the strong law of large numbers, central limit theorem and the law of the iterated logarithm for the partial sums of the Bernoulli random variables.

Suggested Citation

  • James, Barry & James, Kang & Qi, Yongcheng, 2008. "Limit theorems for correlated Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2339-2345, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2339-2345
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    References listed on IDEAS

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    1. C.C. Heyde, 2004. "Asymptotics and Criticality for a Correlated Bernoulli Process," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 46(1), pages 53-57, March.
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    Cited by:

    1. Gava, Renato J. & Rezende, Bruna L.F., 2021. "Some limit theorems for dependent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 170(C).
    2. Zhang, Yang & Zhang, Li-Xin, 2015. "On the almost sure invariance principle for dependent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 264-271.
    3. Alessandro Arlotto & Noah Gans & J. Michael Steele, 2014. "Markov Decision Problems Where Means Bound Variances," Operations Research, INFORMS, vol. 62(4), pages 864-875, August.
    4. Gut, Allan & Stadtmüller, Ulrich, 2022. "The elephant random walk with gradually increasing memory," Statistics & Probability Letters, Elsevier, vol. 189(C).
    5. Zhang, Li-Xin & Zhang, Yang, 2015. "Asymptotics for a class of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 47-56.
    6. Modarres, Reza, 2011. "High-dimensional generation of Bernoulli random vectors," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1136-1142, August.
    7. Wu, Lan & Qi, Yongcheng & Yang, Jingping, 2012. "Asymptotics for dependent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 455-463.
    8. Peter Farkas & Laszlo Matyas, 2015. "Testing for Unit Roots in Panel Data with Boundary Crossing Counts," CEU Working Papers 2015_5, Department of Economics, Central European University, revised 03 Nov 2015.

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