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Maximal inequalities for some dependent sequences and their applications
Shuhe Hu,Xiaoqin Li,Wenzhi Yang,Xuejun Wang 한국통계학회 2011 Journal of the Korean Statistical Society Vol.40 No.1
In this paper, we obtain the maximal inequalities for linear process, ϕ-mixing sequence and linearly negative quadrant dependent (LNQD) sequence when the rth moments of random variables are finite for r > 2. Applying these maximal inequalities above, we get the Hájek–Rényi-type inequality, strong law of large numbers, strong growth rate and integrability of supremum for these three sequences.
Strong limit theorems for weighted sums of NOD sequence and exponential inequalities
Xuejun Wang,Shuhe Hu,Andrei I. Volodin 대한수학회 2011 대한수학회보 Vol.48 No.5
Some properties for negatively orthant dependent sequence are discussed. Some strong limit results for the weighted sums are obtained, which generalize the corresponding results for independent sequence and negatively associated sequence. At last, exponential inequalities for negatively orthant dependent sequence are presented.
STRONG LIMIT THEOREMS FOR WEIGHTED SUMS OF NOD SEQUENCE AND EXPONENTIAL INEQUALITIES
Wang, Xuejun,Hu, Shuhe,Volodin, Andrei I. Korean Mathematical Society 2011 대한수학회보 Vol.48 No.5
Some properties for negatively orthant dependent sequence are discussed. Some strong limit results for the weighted sums are obtained, which generalize the corresponding results for independent sequence and negatively associated sequence. At last, exponential inequalities for negatively orthant dependent sequence are presented.
Exponential inequalities and complete convergence for a LNQD sequence
Wang Xuejun,Hu Shuhe,Yang Wenzhi,Li Xiaoqin 한국통계학회 2010 Journal of the Korean Statistical Society Vol.39 No.4
Some exponential inequalities for a linearly negative quadrant dependent sequence are obtained. By using the exponential inequalities, we give the complete convergence and almost sure convergence for a linearly negative quadrant dependent sequence. In addition,the asymptotic behavior of the probabilities for the partial sums of a linearly negative quadrant dependent sequence is studied.
MAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES
Xuejun, Wang,Shuhe, Hu,Xiaoqin, Li,Wenzhi, Yang Korean Mathematical Society 2011 대한수학회논문집 Vol.26 No.1
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.