168
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

A note on the almost sure central limit theorem for the product of partial sums of m-dependent random variables

&
Pages 2102-2112 | Received 31 May 2017, Accepted 23 Feb 2018, Published online: 16 Apr 2018

References

  • Arnlod, B. C., and J. A. Villaseñor. 1998. The asymptotic distribution of sums of records. Extremes 1 (3):351–63.
  • Berkes, I. 1998. Results and problems related to the pointwise central limit theorem. Asymptotic methods in probability and statistics (Ottawa, ON, 1997), 59–96, North-Holland, Amsterdam.
  • Chen, X. 1997. Moderate deviations for m-dependent random variables with Banach space values. Statist. Probab. Lett. 35 (2):123–34.
  • Chen, X. 1997. The law of the iterated logarithm for m-dependent Banach space valued random variables. J. Appl. Probab. 10 (3):695–732.
  • Chung, K. L. 2001. A course in probability theory. 3rd edition. San Diego, CA: Academic Press, Inc.
  • Gonchigdanzan, K. 2010. Almost sure functional limit theorem for the product of partial sums. ESAIM Probab. Stat. 14:338–42.
  • Gonchigdanzan, K., and G. Rempała. 2006. A note on the almost sure limit theorem for the product of partial sums. Appl. Math. Lett. 19:191–6.
  • Hu, X., and S. Xu. 2007. Almost sure central limit theorem for the product of φ-mixing sums. J. Zhejiang Univ. Sci. Ed. 34 (5):505–8.
  • Jin, J. S. 2007. An almost sure central limit theorem for the product of partial sums of strongly missing random variables. J. Zhejiang Univ. Sci. Ed. 34 (1):24–27.
  • Jin, J. S., J. F. Wang, and L. X. Zhang. 2007. An almost sure limit theorem for products of partial sums of ρ-mixing sequences. Acta Math. Sinica (Chin. Ser.) 50 (4):729–36.
  • Lacey, M. T., and W. Philipp. 1990. A note on the almost sure central limit theorem. Statist. Probab. Lett. 9 (3):201–205.
  • Li, Y. X., and J. F. Wang. 2007. Asymptotic distribution for products of sums under dependence. Metrika 66:75–87.
  • Li, Y. X. 2013. An extension of the almost sure central limit theorem for products of sums under association. Comm. Statist. Theory Methods 42 (3):478–90.
  • Li, Y. X., and J. F. Wang. 2008. An almost sure central limit theorem for products of sums under association. Statist. Probab. Lett. 78 (4):367–75.
  • Miao, Y., and Y. X. Chen. 2011. Some limit theorems of surbvival function estimator for m-dependent processes. Comm. Statist. Theory Methods 40 (12):2193–204.
  • Miao, Y. 2008. Central limit theorem and almost sure central limit theorem for the product of some partial sums. Proc. Indian Acad. Sci. Math. Sci. 118 (2):289–94.
  • Miao, Y., and J. Y. Mu. 2011. Moderate deviations principle for products of sums of random variables. Sci. China Math. 54 (4):769–84.
  • Miao, Y., K. Wang, and F. F. Zhao. 2011. Note on the survival function estimator for m-dependent processes. Pakistan J. Statist. 27 (1):75–9.
  • Miao, Y., and G. Y. Yang. 2008. A moderate deviation principle for m-dependent random variables with unbounded m. Acta Appl. Math. 104 (2):191–9.
  • Peligrad, M., and Q. M. Shao. 1995. A note on the almost sure central limit theorem for weakly dependent random variables. Statist. Probab. Lett. 22 (2):131–6.
  • Resnick, S. I. 1973. Limit laws for record values. Stoch. Pro. Appl. 1:67–82.
  • Rempała, G., and J. Wesołowski. 2002. Asymptotics for products of sums and U-statistics. Elect. Comm. in Probab. 7:47–54.
  • Tan, X. L., Y. Zhang, and Y. Zhang. 2012. An almost sure central limit theorem of products of partial sums for ρ-mixing sequences. J. Inequal. Appl. 2012:51.
  • Wang, J. F., and H. Y. Liang. 2008. A note on the almost sure central limit theorem for negatively associated fields. Statist. Probab. Lett. 78 (13):1964–70.
  • Ye, D. X., and Q. Y. Wu. 2011. Almost sure central limit theorem for product of partial sums of strongly mixing random variables. J. Inequal. Appl., Art. ID 576301.
  • Zhang, L. X., and W. Huang. 2007. A note on the invariance principle of the product of sums of random variables. Electron. Comm. Probab. 12:51–56.
  • Zhu, L. J. 2014. Large deviations for product of sums of random variables. Statist. Probab. Lett. 89:17–22.

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.