Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 88, 2016 - Issue 6
84
Views
1
CrossRef citations to date
0
Altmetric
Articles

A universal result in almost sure central limit theorem for products of sums of partial sums under mixing sequence

Pages 803-812 | Received 13 Jun 2015, Accepted 21 Jan 2016, Published online: 16 Feb 2016

References

  • B.C. Arnold, and J.A. Villaseñor, The asymptotic distribution of sums of records, Extremes 1 (1999), pp. 351–363.
  • K.B. Athreya, and S.G. Pantula, Mixing properties of Harris chains and autoregressive processes, J. Appl. Probab. 23(4) (1986), pp. 880–892.
  • I. Berkes, and E. Csáki, A universal result in almost sure central limit theory, Stochastic Process Appl. 94 (2001), pp. 105–34.
  • P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968.
  • G.A. Brosamler, An almost everywhere central limit theorem, Math. Proc. Cambridge Philos. Soc 104 (1988), pp. 561–574.
  • K. Gonchigdanzan, and G. Rempala, A note on the almost sure limit theorem for the product of partial sums, Appl. Math. Lett. 19 (2006), pp. 191–196.
  • S. Hörmann, An extension of almost surecentral limit theory, Stat. Probab. Lett. 76(2) (2006), pp. 191–202.
  • Y.X. Li, An extension of the almost sure central limit theorem for products of sums under association, Commun. Stat. Theory Methods 42(3) (2013), pp. 478–490.
  • Y.X. Li, and J.F. Wang, An almost sure central limit theorem for products of sums under association, Stat. Probab. Lett. 78(4) (2008), pp. 367–375.
  • Z.Y. Lin and C.R. Lu, Limit Theory for Mixing Dependent Random Variables, Science Press and Kluwer Academic Publishers, Beijing, 1997.
  • X. Lu, and Y. Qi, A note on asymptotic distribution for products of sums, Stat. Probab. Lett. 68 (2004), pp. 407–413.
  • Y. Miao, An extension of almost surecentral limit theory for the product of partial sums, J. Dyn. Syst. Geom. Theor. 7(1) (2009), pp. 49–60.
  • M. Peligrad and P. Reévész, On the almost sure central limit theorem, in Almost Everywhere Convergence, Vol. II, Academic Press, Boston, MA, 1989, pp. 209–225.
  • M. Peligrad, and Q.M. Shao, A note on the almost sure central limit theorem, Stat. Probab. Lett. 22 (1995), pp. 131–136.
  • M. Peligrad, and S. Utev, Central limit theorem for linear process, Ann. Probab. 25 (1997), pp. 443–456.
  • Y. Qi, Limit distributions for products of sums, Stat. Probab. Lett. 62 (2003), pp. 93–100.
  • G. Rempala, and J. Wesolowski, Asymptotic for products of sums and U-statistics, Electron. Commun. Probab. 7 (2002), pp. 47–54.
  • P. Schatte, On strong versions of the central limit theorem, Math. Nachr. 137 (1988), pp. 249–256.
  • B. Tong, Z.X. Peng, and N. Saralees, An extension of almost surecentral limit theorem for order statistics, Extremes 12(3) (2009), pp. 201–209.
  • H. White, and I. Domowitz, Nonlinear regression with dependent observations, Econometric 52 (1984), pp. 143–161.
  • Q.Y. Wu, Almost sure central limit theory for products of sums of partial sums, Appl. Math. J. Chin. Univ. Ser. B 27(2) (2012), pp. 169–180.
  • Y. Zhang, X.Y. Yang, and Z.S. Dong, An almost sure central limit theorem for products of sums of partial sums under association, J. Math. Anal. Appl. 355 (2009), pp. 708–716.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.