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A NOTE ON THE COMPLETE MOMENT CONVERGENCE FOR ARRAYS OF B-VALUED RANDOM VARIABLES

  • Wu, Yongfeng (College of Mathematics and Computer Science Tongling University) ;
  • Song, Mingzhu (College of Mathematics and Computer Science Tongling University)
  • Received : 2014.03.01
  • Published : 2015.05.31

Abstract

In this article, we discuss the complete moment convergence for arrays of B-valued random variables. We obtain some new results which improve the corresponding ones of Sung and Volodin [17].

Keywords

References

  1. A. de Acosta, Inequalities for B-valued random vectors with applications to the strong law of large numbers, Ann. Probab. 9 (1981), no. 1, 157-161. https://doi.org/10.1214/aop/1176994517
  2. S. E. Ahmed, R. Giuliano Antonini, and A. Volodin, On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements with application to moving avurage processes, Statist. Probab. Lett. 58 (2002), no. 2, 185-194. https://doi.org/10.1016/S0167-7152(02)00126-8
  3. L. E. Baum and M. Katz, Convergence rates in the law of large numbers, Trans. Am. Math. Soc. 120 (1965), 108-123. https://doi.org/10.1090/S0002-9947-1965-0198524-1
  4. Y. S. Chow, On the rate of moment convergence of sample sums and extremes, Bull. Inst. Math. Acad. Sinica 16 (1988), no. 3, 177-201.
  5. A. Gut, Complete convergence for arrays, Period. Math. Hungar. 25 (1992), no. 1, 51-75. https://doi.org/10.1007/BF02454383
  6. P. L. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. USA 33 (1947), 25-31. https://doi.org/10.1073/pnas.33.2.25
  7. T. C. Hu, D. Li, A. Rosalsky, and A. Volodin, On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements, Theory Probab. Appl. 47 (2002), no. 3, 455-468.
  8. T. C. Hu, A. Rosalsky, D. Szynal, and A. Volodin, On complete convergence for arrays of rowwise independent random elements in Banach spaces, Stochastic Anal. Appl. 17 (1999), no. 6, 963-992. https://doi.org/10.1080/07362999908809645
  9. T. S. Kim and M. H. Ko, On the complete convergence of moving average process with Banach space valued random elements, J. Theoret. Probab. 21 (2008), no. 2, 431-436. https://doi.org/10.1007/s10959-007-0118-6
  10. T. S. Kim and M. H. Ko, Complete moment convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 78 (2008), no. 7, 839-846. https://doi.org/10.1016/j.spl.2007.09.009
  11. D. Li, M. B. Rao, T. F. Ting, and X. C. Wang, Complete convergence and almost sure convergence of weighted sums of random variables, J. Theoret. Probab. 8 (1995), no. 1, 49-76. https://doi.org/10.1007/BF02213454
  12. Y. X. Li and L. X. Zhang, Complete moment convergence of moving-average processes under dependence assumptions, Statist. Probab. Lett. 70 (2004), no. 3, 191-197. https://doi.org/10.1016/j.spl.2004.10.003
  13. H. Y. Liang, D. L. Li, and A. Rosalsky, Complete moment and integral convergence for sums of negatively associated random variables, Acta Math. Sin. (Engl. Ser.) 26 (2010), no. 3, 419-432. https://doi.org/10.1007/s10114-010-8177-5
  14. D. H. Qiu, T. C. Hu, M. O. Cabrera, and A. Volodin, Complete convergence for weighted sums of arrays of Banach-space-valued random elements, Lith. Math. J. 52 (2012), no. 3, 316-325. https://doi.org/10.1007/s10986-012-9175-3
  15. S. H. Sung, Complete convergence for weighted sums of arrays of rowwise independent B-valued random variables, Stochastic Anal. Appl. 15 (1997), no. 2, 255-267. https://doi.org/10.1080/07362999708809474
  16. S. H. Sung, Moment inequalities and complete moment convergence, J. Inequal. Appl. 2009 (2009), Article ID 271265, doi:10.1155/2009/271265.
  17. S. H. Sung and A. Volodin, A note on the rate of complete convergence for weighted sums of arrays of Banach space valued random elements, Stochastic Anal. Appl. 29 (2011), no. 2, 282-291. https://doi.org/10.1080/07362994.2011.548670
  18. D. C. Wang and C. Su, Moment complete convergence for sequences of B-valued iid random elements, Acta Math. Appl. Sin. 27 (2004), no. 3, 440-448.
  19. D. C. Wang and W. Zhao, Moment complete convergence for sums of a sequence of NA random variables, Appl. Math. J. Chinese Univ. Ser. A 21 (2006), no. 4, 445-450.
  20. X. Wang, M. B. Rao, and X. Yang, Convergence rates on strong laws of large numbers for arrays of rowwise independent elements, Stochastic Anal. Appl. 11 (1993), no. 1, 115-132. https://doi.org/10.1080/07362999308809305
  21. Y. F. Wu, Convergence properties of the maximal partial sums for arrays of rowwise NA random variables, Theory Probab. Appl. 56 (2012), no. 3, 527-535. https://doi.org/10.1137/S0040585X97985583
  22. L. X. Zhang, Complete convergence of moving average processes under dependence as-sumptions, Statist. Probab. Lett. 30 (1996), no. 2, 165-170. https://doi.org/10.1016/0167-7152(95)00215-4