On the Strong Laws for Weighted Sums of -Mixing Random Variables

Abstract

Complete convergence is studied for linear statistics that are weighted sums of identically distributed ρ * -mixing random variables under a suitable moment condition. The results obtained generalize and complement some earlier results. A Marcinkiewicz-Zygmund-type strong law is also obtained.

On the strong convergence for weighted sums of asymptotically almost negatively associated random variables

“…We use different methods from those of Sung [8]. The obtained results not only extend the corresponding results of Zhou et al [25], Sung [8,9] to AANA case, but also improve them.…”

“…Furthermore, suppose that EX = 0 when 1 < α ≤ 2. If Recently, Zhou et al [25] generalized the above Theorem 1.1 to the case ρ * -mixing random variables when α = γ by using different methods from those of Sung [8].…”

On Strong Convergence for Weighted Sums of a Class of Random Variables

“…As an application, the Marcinkiewicz-Zygmund-type strong law of large numbers is obtained. Our result generalizes the corresponding one of Zhou et al (2011) and improves the corresponding one of .…”

“…Let { , , ≥ 1} be a sequence of identically distributed random variables and { ,1 ≤ ≤ , ≥ 1} an array of constants. The strong convergence results for weighted sums ∑ =1 have been studied by many authors; see, for example, Choi and Sung [1], Cuzick [2], Wu [3], Bai and Cheng [4], Chen and Gan [5], Cai [6], Sung [7,8], Shen [9], Wang et al [10][11][12][13][14], Zhou et al [15], Wu [16][17][18], Xu and Tang [19], and so forth. Many useful linear statistics are these weighted sums.…”

Further study on complete convergence for weighted sums of arrays of rowwise asymptotically almost negatively associated random variables

“…For more details about the strong convergence theorems for weighted sums of dependent sequences, one can refer to Cai [4], Jing and Liang [10], Zhou et al [27], Wang et al [21], Huang and Wang [9], Shen and Wu [13], Sung [16,17], and so on.…”