The Convergence Theorems for Mixing Random Variable Sequences

In this paper, some limit properties for mixing random variables sequences were studied and some results on weak law of large number for mixing random variables sequences were presented. Some complete convergence theorems were also obtained. The results extended and improved the corresponding theorems in i.i.d random variables sequences.

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References:
[1] L. X. Zhang and X. Y, Wang, “Convergence rates in the strong laws of asymptotically negatively associated random fields,” Appl. Math. J. Chinese Univ, Ser. B. vol. 14, pp. 406–416,1999.
[2] Joag- K. Dev, F. Proschan, “Negative association of random variables with applications.” Ann. Statist, vol. 11, pp. 286–295, 1983.
[3] C. Su, T. Jiang, Q. H. Tang and H. Y. Liang, “The safety of negatively associated dependence structure,” Chinese J. Appl. Probab. Statist, .vol. 18.pp. 400–404, 2002.
[4] H. Zhou, “Moment inequalities and application for mixing sequence,” Journal of Zhejiang University, vol. 16, pp. 691–710, 2000.
[5] L. X. Zhang, “Central limit theorems for asymptotically negatively associated random fields,” Acta. Math. Sinica, vol. 14, pp. 406–416, 1999.
[6] L. X. Zhang, “A functional central limit theorem for asymptotically negatively associated random fields,” Acta. Math. Hungar, vol. 83, pp. 237–259, 2000.
[7] J. F. Wang and F. B. Lu, “Inequalities of maximum of partial sums and weak convergence for a class of weak dependent random variables,” Acta. Math. Sinica. vol. 22, pp. 693–700,2006.
[8] X. Chen and Y. C. Wu, “Strong consistency of M-estimator in nonlinear models under mixing errors,” Journal of Chongqing University of Arts and Sciences, vol. 29. pp. 5–9, 2010.
[9] W. Feller, “A limit theorem for random variables with infinite moments,” American Journal of Mathematics. vol. 68, pp.257–262, 1946.
[10] L. E Baum and M. Katz, “Convergence rates in the law of large numbers,” Transactions of the American Mathematical Society. vol. 120, pp. 108–123, 1965.
[11] C. Y. Lu and Z. Y. Lin, The limiting theory of mixing-dependent random variables. China: Academic Press, 1997, ch 4-6.