Strong laws for weighted sums of random variables satisfying generalized Rosenthal type inequalities

Journal of inequalities and applications

article

Yanchun Yi¹  Pingyan Chen²  Soo Hak Sung³ 

[1] College of Math. and Statist., Hengyang Normal University;Department of Mathematics, Jinan University;Department of Applied Mathematics, Pai Chai University

关键词: Strong law of large numbers;    Weighted sum;    Widely orthant dependent random variable;   

DOI  :  10.1186/s13660-020-02311-1

学科分类：电力

来源: SpringerOpen

【 摘 要 】

Let $1\le p<2$ and $0<\alpha , \beta <\infty $ with $1/p=1/\alpha +1/\beta $. Let $\{X_{n}, n\ge 1\}$ be a sequence of random variables satisfying a generalized Rosenthal type inequality and stochastically dominated by a random variable X with $E|X|^{\beta }< \infty $. Let $\{a_{nk}, 1\le k\le n, n\ge 1\}$ be an array of constants satisfying $\sum_{k=1}^{n} |a_{nk}|^{\alpha }=O(n)$. 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).

【 授权许可】

CC BY