期刊：
JOURNAL OF MATHEMATICAL INEQUALITIES,2021年15(4):1533-1544 ISSN：1846-579X
通讯作者：
Sung, Soo Hak
作者机构：
[Yi Yanchun] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Peoples R China.;[Chen, Pingyan] Jinan Univ, Dept Math, Guangzhou 510630, Peoples R China.;[Sung, Soo Hak] Pai Chai Univ, Dept Appl Math, Daejeon 35345, South Korea.
通讯机构：
[Sung, Soo Hak] P;Pai Chai Univ, Dept Appl Math, Daejeon 35345, South Korea.
关键词：
Strong consistency;simple linear errors-in-variables regression model;widely orthant dependent random variable
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2020年2020(1):1-8 ISSN：1029-242X
通讯作者：
Sung, Soo Hak
作者机构：
[Yi, Yanchun] Hengyang Normal Univ, Coll Math & Stat, Hengyang, Peoples R China.;[Chen, Pingyan] Jinan Univ, Dept Math, Guangzhou, Peoples R China.;[Sung, Soo Hak] Pai Chai Univ, Dept Appl Math, Daejeon, South Korea.
通讯机构：
[Sung, Soo Hak] P;Pai Chai Univ, Dept Appl Math, Daejeon, South Korea.
关键词：
Strong law of large numbers;Weighted sum;Widely orthant dependent random variable
摘要：
<jats:title>Abstract</jats:title><jats:p>Let <jats:inline-formula><jats:alternatives><jats:tex-math>$1\le p<2$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>p</mml:mi><mml:mo><</mml:mo><mml:mn>2</mml:mn></mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$0<\alpha , \beta <\infty $</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>0</mml:mn><mml:mo><</mml:mo><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>β</mml:mi><mml:mo><</mml:mo><mml:mi>∞</mml:mi></mml:math></jats:alternatives></jats:inline-formula> with <jats:inline-formula><jats:alternatives><jats:tex-math>$1/p=1/\alpha +1/\beta $</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>α</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>β</mml:mi></mml:math></jats:alternatives></jats:inline-formula>. Let <jats:inline-formula><jats:alternatives><jats:tex-math>$\{X_{n}, n\ge 1\}$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>{</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mn>1</mml:mn><mml:mo>}</mml:mo></mml:math></jats:alternatives></jats:inline-formula> be a sequence of random variables satisfying a generalized Rosenthal type inequality and stochastically dominated by a random variable <jats:italic>X</jats:italic> with <jats:inline-formula><jats:alternatives><jats:tex-math>$E|X|^{\beta }< \infty $</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>E</mml:mi><mml:msup><mml:mrow><mml:mo>|</mml:mo><mml:mi>X</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mi>β</mml:mi></mml:msup><mml:mo><</mml:mo><mml:mi>∞</mml:mi></mml:math></jats:alternatives></jats:inline-formula>. Let <jats:inline-formula><jats:alternatives><jats:tex-math>$\{a_{nk}, 1\le k\le n, n\ge 1\}$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>{</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>k</mml:mi><mml:mo>≤</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mn>1</mml:mn><mml:mo>}</mml:mo></mml:math></jats:alternatives></jats:inline-formula> be an array of constants satisfying <jats:inline-formula><jats:alternatives><jats:tex-math>$\sum_{k=1}^{n} |a_{nk}|^{\alpha }=O(n)$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:msubsup><mml:msup><mml:mrow><mml:mo>|</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:mi>α</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:math></jats:alternatives></jats:inline-formula>. Marcinkiewicz–Zygmund type strong laws for weighted sums of the random variables are established. Our results generalize or improve the corresponding ones of Wu (J. Inequal. Appl. 2010:383805, 2010), Huang et al. (J. Math. Inequal. 8:465–473, 2014), and Wu et al. (Test 27:379–406, 2018).</jats:p>
作者机构：
School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangdong, 510320;Department of Mathematics and Computional Science, Hengyang Normal University, Hunan, 421008;Department of Mathematics, Jinan University(Guangdong), Guangdong, 510630
摘要：
In this paper, the complete convergence theorems for Sung’s type weighted sums of END random variables and PNQD random variables with general moment conditions are obtained. The theorems extend the related known works in the literature.
关键词：
NOD sequence;Stout's type weighted sum;complete convergence
摘要：
In this paper, the complete convergence for the weighted sums of independent and identically distributed random variables in Stout [9] is improved and extended under NOD setup. The more optimal moment condition is given. The main results also hold for END sequence.
作者机构：
[Yi Yanchun] Department of Mathematics and Computional Science, Hengyang Normal University;[Qiu Dehua] School of Mathematics and Statistics, Guangdong University of Finance and Economics
关键词：
Kolmogorov-Feller type weak law of large numbers;negatively associated random variables;independent identically distributed random variables
摘要：
In this paper, the Kolmogorov-Feller type weak law of large numbers are obtained, which extend and improve the related known works in the literature.
