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Asymptotics for dependent Bernoulli random variables

Author

Listed:
  • Wu, Lan
  • Qi, Yongcheng
  • Yang, Jingping

Abstract

This paper considers a sequence of Bernoulli random variables which are dependent in a way that the success probability of a trial conditional on the previous trials depends on the total number of successes achieved prior to the trial. The paper investigates almost sure behaviors for the sequence and proves the strong law of large numbers under weak conditions. For linear probability functions, the paper also obtains the strong law of large numbers, the central limit theorems and the law of the iterated logarithm, extending the results by James et al. (2008).

Suggested Citation

  • Wu, Lan & Qi, Yongcheng & Yang, Jingping, 2012. "Asymptotics for dependent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 455-463.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:3:p:455-463
    DOI: 10.1016/j.spl.2011.12.002
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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.
    2. 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.
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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. Zhang, Li-Xin & Zhang, Yang, 2015. "Asymptotics for a class of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 47-56.

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