Strong Laws of Large Numbers for Arrays of Rowwise Conditionally Negatively Dependent Random Variables

DOI: 10.4236/apm.2013.37081   PDF   HTML   XML   3,199 Downloads   4,678 Views  

Abstract

Let {Xnk} be an array of rowwise conditionally negative dependent random variables. Complete convergence of to 0 is obtained by using various conditions on the moments and conditional means.

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R. Patterson, T. Royal-Thomas and W. Patterson, "Strong Laws of Large Numbers for Arrays of Rowwise Conditionally Negatively Dependent Random Variables," Advances in Pure Mathematics, Vol. 3 No. 7, 2013, pp. 625-626. doi: 10.4236/apm.2013.37081.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[2] R. Patterson, R. L. Taylor and A. Bozorgnia, “Chung Type Stong Laws for Arrays of Random Elements and Bootstrapping,” Stochastic Analysis and Applications, Vol. 15, No. 5, 1997, pp. 651-669.
http://dx.doi.org/10.1080/07362999708809501
[3] P. L. Hu and H. Robbins, “Complete Convergence and the Law of Large Numbers,” Proceedings of the National Academy of Sciences of the United States of America, Vol. 33, No. 2, 1947, pp. 25-31.
http://dx.doi.org/10.1073/pnas.33.2.25
[4] R. Patterson, R. L. Taylor and A. Bozorgnia, “Strong Laws of Large Numbers for Arrays of Rowwise Conditionally Independent Random Variables,” Journal of Applied Mathematics and Stochastic Analysis, Vol. 6, No. 1, 1993, pp. 1-10.
http://dx.doi.org/10.1155/S1048953393000012

  
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