Equivalent conditions of complete convergence for weighted sums of ANA random variables

2018 ◽  
Vol 68 (6) ◽  
pp. 1495-1505
Author(s):  
Haiwu Huang
Keyword(s):  
Convergence Theorem ◽  
Complete Convergence ◽  
Random Variables ◽  
Weighted Sums ◽  
Negatively Associated ◽  
Complete Convergence Theorem ◽  
Equivalent Conditions

Abstract In this paper, the author investigates the complete convergence for weighted sums of asymptotically negatively associated (ANA) random variables with different distributions, and obtains some equivalent conditions of complete convergence theorem for weighted sums as well as summation of ANA cases. These results generalize and improve the corresponding ones obtained by Baum and Katz (1965), Peligrad and Gut (1999) and Cai (2006), respectively.

scholarly journals Complete Convergence for Weighted Sums of Widely Acceptable Random Variables under Sublinear Expectations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Rong Hu ◽  
Qunying Wu
Keyword(s):  
Convergence Theorem ◽  
Probability Space ◽  
Complete Convergence ◽  
Choquet Integral ◽  
Random Variables ◽  
Weighted Sums ◽  
Sublinear Expectation ◽  
Acceptable Random Variables ◽  
Complete Convergence Theorem

Using different methods than the probability space, under the condition that the Choquet integral exists, we study the complete convergence theorem for weighted sums of widely acceptable random variables under sublinear expectation space. We proved corresponding theorem which was extended to the sublinear expectations’ space from the probability space, and similar results were obtained.

scholarly journals Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums ofρ~-Mixing Random Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Chongfeng Lan
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Strong Law ◽  
Large Numbers ◽  
Sufficient And Necessary Conditions ◽  
Complete Convergence Theorem ◽  
Mixing Random Variables ◽  
Equivalent Conditions

The equivalent conditions of complete convergence are established for weighted sums ofρ~-mixing random variables with different distributions. Our results extend and improve the Baum and Katz complete convergence theorem. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequence ofρ~-mixing random variables is obtained.

scholarly journals Complete Convergence for Arrays of Rowwise Asymptotically Almost Negatively Associated Random Variables

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Xuejun Wang ◽  
Shuhe Hu ◽  
Wenzhi Yang
Keyword(s):  
Complete Convergence ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Weighted Sums ◽  
Strong Law ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Negatively Associated Random Variables ◽  
Large Numbers ◽  
Asymptotically Almost Negatively Associated

Let{Xni,i≥1,n≥1}be an array of rowwise asymptotically almost negatively associated random variables. Some sufficient conditions for complete convergence for arrays of rowwise asymptotically almost negatively associated random variables are presented without assumptions of identical distribution. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of asymptotically almost negatively associated random variables is obtained.

On the strong convergence forweighted sums of negatively superadditive dependent random variables

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 295-308
Author(s):  
Lulu Zheng ◽  
Xuejun Wang ◽  
Wenzhi Yang
Keyword(s):  
Strong Convergence ◽  
Complete Convergence ◽  
Random Variables ◽  
Maximal Inequality ◽  
Weighted Sums ◽  
Exponential Inequality ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Identical Distribution ◽  
Nsd Random Variables

In this paper, we present some results on the complete convergence for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables by using the Rosenthal-type maximal inequality, Kolmogorov exponential inequality and the truncation method. The results obtained in the paper extend the corresponding ones for weighted sums of negatively associated random variables with identical distribution to the case of arrays of rowwise NSD random variables without identical distribution.

scholarly journals Equivalent Conditions of Complete Convergence for Weighted Sums of Sequences of Negatively Dependent Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Mingle Guo
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Weighted Sums ◽  
Moment Inequality ◽  
Dependent Random Variables ◽  
Negatively Dependent Random Variables ◽  
Equivalent Conditions

The complete convergence for weighted sums of sequences of negatively dependent random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete convergence for weighted sums of sequences of negatively dependent random variables are established. These results not only extend the corresponding results obtained by Li et al. (1995), Gut (1993), and Liang (2000) to sequences of negatively dependent random variables, but also improve them.

Complete Convergence of Weighted Sums of ρ Mixing Sequences

2014 ◽  
Vol 651-653 ◽  
pp. 2134-2137
Author(s):  
Quan Yu Ren ◽  
Xia Dan
Keyword(s):  
Complete Convergence ◽  
Random Variable ◽  
Weighted Sums ◽  
Uniform Integrability ◽  
Probability Limit ◽  
Limit Theory ◽  
Mixing Sequences ◽  
Complete Convergence Theorem ◽  
Mixing Sequence ◽  
Equivalent Conditions

Probability limit theory is not only one of the main branches of probability theory, but also important base of others branches and mathematical statistics. In this paper, we discuss the laws of large number and complete convergence of mixing sequence. The paper can be divided into the following two parts. In the first part, we introduce Cesáro uniform integrability and equivalent conditions for sequences of random variable. Then, under these conditions, we establish the weak law of large number and convergence for weighted sums of sequences of random variable of mixing sequence. As an especial example, we obtain the weak law of large number or convergence for mixing sequence. From the course, we can find that Cesáro uniform integrability is also an effective tool for researching the weak law of large number of mixing sequence .In the second part, we investigate a complete convergence theorem of weighted sums of mixing sequence, and prove that the existent results are especial examples for it.

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