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1.
Let {X n , n ≥ 1} be an arbitrary sequence of random variables. Some convergence results for the partial sums of arbitrary sequence of random variables are obtained, which generalize the known results for independent sequences, NA sequences, ρ-mixing sequences and φ-mixing sequences, and so on. 相似文献
2.
Complete Convergence and Complete Moment Convergence for Maximal Weighted Sums of Extended Negatively Dependent Random Variables
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Ji Gao Yan 《数学学报(英文版)》2018,34(10):1501-1516
In this paper,the complete convergence and complete moment convergence for maximal weighted sums of extended negatively dependent random variables are investigated.Some sufficient conditions for the convergence are provided.In addition,the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of extended negatively dependent random variables is obtained.The results obtained in the article extend the corresponding ones for independent random variables and some dependent random variables. 相似文献
3.
《数学季刊》2016,(1):1-8
In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent ran-dom variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables. 相似文献
4.
In this paper, we discuss the complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables. By applying moment inequality and truncation methods, the sufficient conditions of complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables are established. These results generalize and complement some known conclusions. 相似文献
5.
Complete and complete moment convergence for weighted sums of widely orthant dependent random variables 总被引:1,自引:0,他引:1
In this paper, we establish a complete convergence result and a complete moment convergence result for weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the corresponding results for weighted sums of extended negatively orthant dependent random variables are also obtained, which generalize and improve the related known works in the literature. 相似文献
6.
Inequalities of Maximum of Partial Sums and Weak Convergence for a Class of Weak Dependent Random Variables 总被引:11,自引:0,他引:11
Jiang Feng WANG Feng Bin LU 《数学学报(英文版)》2006,22(3):693-700
In this paper, we establish a Rosenthal-type inequality of the maximum of partial sums for ρ^- -mixing random fields. As its applications we get the Hájeck -Rènyi inequality and weak convergence of sums of ρ^- -mixing sequence. These results extend related results for NA sequence and p^* -mixing random fields, 相似文献
7.
By using Rosenthal type moment inequality for extended negatively dependent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively dependent random variables under more general conditions. These results complement and improve the corresponding results obtained by Li et al.(Li D L, RAO M B, Jiang T F, Wang X C. Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab., 1995, 8: 49–76) and Liang(Liang H Y. Complete convergence for weighted sums of negatively associated random variables. Statist.Probab. Lett., 2000, 48: 317–325). 相似文献
8.
In this paper, the complete convergence and strong law of large numbers for weighted sums of(φ)-mixing sequence with different distribution are investigated under some weaker moment conditions. Our results extend ones of independent sequence with identical distribution to the case of(φ)-mixing sequence with different distribution. 相似文献
9.
《数学季刊》2016,(4):359-368
In the paper, the complete convergence for the maximum of weighted sums of negatively superadditive dependent(NSD, in short) random variables is investigated by using the Rosenthal type inequality. Some su?cient conditions are presented to prove the complete convergence. The result obtained in the paper generalizes some corresponding ones for independent random variables and negatively associated random variables. 相似文献
10.
《数学季刊》2017,(2)
In this paper, the complete convergence and strong law of large numbers for weighted sums of φ-mixing sequence with different distribution are investigated under some weaker moment conditions. Our results extend ones of independent sequence with identical distribution to the case of φ-mixing sequence with different distribution. 相似文献
11.
Complete Convergence for Weighted Sums of Negatively Superadditive Dependent Random Variables
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Let $\{X_n,n\geq1\}$ be a sequence of negatively superadditive
dependent (NSD, in short) random variables and $\{a_{nk}, 1\leq
k\leq n, n\geq1\}$ be an array of real numbers. Under some suitable
conditions, we present some results on complete convergence for
weighted sums $\sum_{k=1}^na_{nk}X_k$ of NSD random variables by
using the Rosenthal type inequality. The results obtained in the
paper generalize some corresponding ones for independent random
variables and negatively associated random variables. 相似文献
12.
In this paper, the authors discuss the moment
complete convergence for weighted sums of -mixing random
variables, and obtains the sufficient condition for moment complete
convergence of -mixing sequence under some mixing rate
condition, which generalize the result of moment complete
convergence for weighted sums of i.i.d. random variables to
-mixing random variables. 相似文献
13.
Lu Chuanrong 《数学年刊B辑(英文版)》1984,5(4):731-736
In this paper, the author improves Yoshihara''s result(J.Multivariate Anal. 8(1978),584-588) and proves the weak convergence of empirical processes for sequence of p-mixing strictly stationary random variable with $\[\rho (n) = O({n^{ - \frac{1}{2} - \theta }}),\theta > 0\]$.
Moreover, the author simplifies the complex proof of weak convergence of empirical processes wwith random index and gets the corresponding result for $\[\alpha \]$-mixing stationary random variables. 相似文献
14.
In this article, applying the result of complete convergence for negatively associated (NA) random variables which is obtained by Chen et al.\ucite{14}, the equivalent conditions of complete convergence for weighted sums of arrays of row-wise negatively associated random variables is investigated. As a result, the corresponding results of Liang\ucite{11} is generalized, moreover, the proof procedure is simplified greatly which is different from truncation method of Liang's. Thus, Gut's\ucite{13} result on Ces\`{a}ro summation of i.i.d. random variables is extended. 相似文献
15.
In this paper, the complete qth moment convergence for weighted sums of sequences of negatively orthant dependent random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete qth moment convergence for weighted sums of sequences of negatively orthant dependent random variables are established. These results not only extend the corresponding results obtained by Li and Sp\v{a}taru\ucite{4}, Liang et al.\ucite{5}, Guo\ucite{6} and Gut\ucite{21} to sequences of negatively orthant dependent random variables, but also improve them. 相似文献
16.
In this paper, we obtain theorems of complete convergence and strong laws of large numbers for weighted sums of sequences of independent random elements in a Banach space of type p (1 ≤ p ≤ 2). The results improve and extend the corresponding results on real random variables obtained by [1] and [2]. 相似文献
17.
18.
Negatively associated (NA) random variables are a more general class of random variables which include a set of independent random variables and have been applied to many practical fields. In this paper, the complete moment convergence of weighted sums for arrays of row-wise NA random variables is investigated. Some sufficient conditions for complete moment convergence of weighted sums for arrays of row-wise NA random variables are established. Moreover, under the weaker conditions, we extend the results of Baek et al. [J. Korean Stat. Soc. 37 (2008), pp. 73–80] and Sung [Abstr. Appl. Anal. 2011 (2011)]. As an application, the complete moment convergence of moving average processes based on an NA random sequence is obtained, which improves the result of Li and Zhang [Stat. Probab. Lett. 70 (2004), pp. 191–197 ]. 相似文献