A note on the rates of convergence for weighted sums of ρ * -mixing random variables

Complete moment convergence for Sung’s type weighted sums of ρ*-mixing random variables

“…A number of limit results for ρ * -mixing sequence of random variables have been established by many authors. We refer to Bradley [4] for the central limit theorem, Bryc and Smolenski [5], Peligrad and Gut [16], and Utev and Peligrad [21] for the moment inequalities, Chen and Liu [8] (see Remak 1 on page 289) for the complete moment convergence, and Sung [19], Wang et al [24], and Wu et al [27] for the complete convergence of weighted sums. Now we state the main result.…”

On complete moment convergence for weighted sums of AANA random variables

“…(Wu, Sung and Volodin [18]) Let {a ni , i ≥ 1, n ≥ 1} be an array of real constants satisfying (1.1) for some α > 0, and X be a random variable. Let…”

Complete Moment Convergence for Sung’s Type Weighted Sums ofB-Valued Random Elements

“…The complete convergence, the complete moment convergence, and the refined result of complete convergence have attracted many authors. We refer to Bai and Su [14], Baum and Katz [15], Chen [16], Chen et al [17,18], Chen and Wang [10], Katz [19], Li and Spȃ taru [11,20], Qiu et al [21], Rosalsky et al [22], Sung [23], Wang and Su [24], and Wu et al [25].…”