MAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES

• Xuejun, Wang (SCHOOL OF MATHEMATICAL SCIENCE ANHUI UNIVERSITY) ;
• Shuhe, Hu (SCHOOL OF MATHEMATICAL SCIENCE ANHUI UNIVERSITY) ;
• Xiaoqin, Li (SCHOOL OF MATHEMATICAL SCIENCE ANHUI UNIVERSITY) ;
• Wenzhi, Yang (SCHOOL OF MATHEMATICAL SCIENCE ANHUI UNIVERSITY)
• Published : 2011.01.31

Abstract

Let {$X_n$, $n{\geq}1$} be a sequence of asymptotically almost negatively associated random variables and $S_n=\sum^n_{i=1}X_i$. In the paper, we get the precise results of H$\acute{a}$jek-R$\acute{e}$nyi type inequalities for the partial sums of asymptotically almost negatively associated sequence, which generalize and improve the results of Theorem 2.4-Theorem 2.6 in Ko et al. ([4]). In addition, the large deviation of $S_n$ for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.

Acknowledgement

Supported by : NNSF of China, Anhui Colleges, Anhui University

References

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3. Maximal inequalities and strong law of large numbers for sequences of m-asymptotically almost negatively associated random variables vol.46, pp.6, 2017, https://doi.org/10.1080/03610926.2015.1048885
4. Strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables vol.109, pp.1, 2015, https://doi.org/10.1007/s13398-014-0174-6
5. Strong Convergence Properties and Strong Stability for Weighted Sums of AANA Random Variables vol.2013, 2013, https://doi.org/10.1155/2013/295041
6. Lr convergence for arrays of rowwise asymptotically almost negatively associated random variables 2017, https://doi.org/10.1080/03610926.2017.1285932
7. Some strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-4