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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:70428", author = "Yan-zhao Yang", title = "The Convergence Theorems for Mixing Random Variable Sequences", abstract = "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.", keywords = "Complete convergence, mixing random variables,
weak law of large numbers.", volume = "9", number = "2", pages = "123-4", }