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Communications in Statistics - Theory and Methods Volume 49, 2020 - Issue 13
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Original Articles

Some extensions of the classical law of large numbers

Huanhuan MaDepartment of Statistics, School of Economics, Jinan Univeristy, Guangzhou, China; ;College of Mathematics and Information Science, Henan Normal University, Henan Province, China; View further author information
,
Yan SunScience College, Beijing Information Science and Technology University, Beijing, China; View further author information
&
Yu MiaoCollege of Mathematics and Information Science, Henan Normal University, Henan Province, ChinaCorrespondence[email protected]
View further author information
Pages 3228-3237 | Received 27 Sep 2018, Accepted 20 Feb 2019, Published online: 14 Apr 2019

References

  • Chen, Z. J., P. Y. Wu, and B. M. Li. 2013. A strong law of large numbers for non-additive probabilities. International Journal of Approximate Reasoning 54 (3):365–77. doi:10.1016/j.ijar.2012.06.002.
  • Hoffmann-Jørgensen, J., Y. Miao, X. C. Li, and S. F. Xu. 2016. Kolmogorov type law of the logarithm for arrays. Journal of Theoretical Probability 29 (1):32–47. doi:10.1007/s10959-014-0574-8.
  • Hu, S. H. 2003. Some new results for the strong law of large numbers. Acta Mathematica Sinica. Chinese Series 46 (6):1123–34.
  • Hu, S. H., and M. Hu. 2006. A general approach rate to the strong law of large numbers. Statistics & Probability Letters 76 (8):843–51.
  • James, B., K. James, and Y. C. Qi. 2008. Limit theorems for correlated Bernoulli random variables. Statistics & Probability Letters 78 (15):2339–45. doi:10.1016/j.spl.2008.01.104.
  • Kruglov, V. M. 2011. A generalization of weak law of large numbers. Stochastic Analysis and Applications 29 (4):674–83. doi:10.1080/07362994.2011.581099.
  • Lin, Z. Y., and Z. D. Bai. 2010. Probability inequalities. Beijing: Science Press Beijing; Heidelberg: Springer.
  • Loève, M. 1977. Probability theory. I. 4th ed. Graduate texts in mathematics. vol. 45. New York-Heidelberg: Springer-Verlag.
  • Miao, Y., G. Y. Yang, and G. Stoica. 2015. On the rate of convergence in the strong law of large numbers for martingales. Stochastics 87 (2):185–98. doi:10.1080/17442508.2014.938075.
  • Miao, Y., J. Y. Mu, and J. Xu. 2017. An analogue for Marcinkiewicz-Zygmund strong law of negatively associated random variables. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 111 (3):697–705. doi:10.1007/s13398-016-0320-4.
  • Miao, Y., W. F. Xu, S. S. Chen, and A. Adler. 2014. Some limit theorems for negatively associated random variables. Proceedings - Mathematical Sciences 124 (3):447–56. doi:10.1007/s12044-014-0185-4.
  • Ren, C. G., S. H. Hu, X. Li, and X. T. Liu. 2011. Some improvements of an extended Borel strong law of large numbers. Journal of Anhui University. Natural Science Edition 35 (3):25–8.
  • Zhang, Y., and L. X. Zhang. 2017. Limit theorems for dependent Bernoulli variables with statistical inference. Communications in Statistics. Theory and Methods 46 (4):1551–9. doi:10.1080/03610926.2015.1021015.

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