Complete convergence and complete moment convergence for weighted sums of extended negatively dependent random variables under sub-linear expectation

Abstract

In this paper, we study the complete convergence and complete moment convergence for weighted sums of extended negatively dependent (END) random variables under sub-linear expectations space with the condition of , further , ( is a slow varying and monotone nondecreasing function). As an application, the Baum-Katz type result for weighted sums of extended negatively dependent random variables is established under sub-linear expectations space. The results obtained in the article are the extensions of the complete convergence and complete moment convergence under classical linear expectation space.

Equivalent Conditions of Complete p th Moment Convergence for Weighted Sums of I. I. D. Random Variables under Sublinear Expectations

“…e interested reader could refer to Xu and Zhang [8,9], Chen [10], Gao and Xu [11], Fang et al [12], Hu et al [13], Hu and Yang [14], Huang and Wu [15], Kuczmaszewska [16], Ma and Wu [17], Wang and Wu [18], Wu and Jiang [19], Yu and Wu [20], Zhang [21], Zhong and Wu [22], and references therein for more limit theorems under sublinear expectations.…”

Convergence for sums of i.i.d. random variables under sublinear expectations

“…(ii) As in the proof of Lemma 2.2 in Zhong and Wu [16], let Z(x) = x (β+1)/γ +α ln(1 + x), and let Z -1 (x) be the inverse function of Z(x). Then…”

“…Zhang [12][13][14] obtained important inequalities including exponential and Rosenthal's inequalities and studied Donsker's invariance principle under sublinear expectations. Inspired by the works of Zhang [12][13][14][15], Huang and Wu [5] and Zhong and Wu [16] studied some limits theorems under sublinear expectation space. Recently, under sublinear expectations, Wu [10] proved precise asymptotics for complete integral convergence, and Xu and Cheng [11] established precise asymptotics in the law of iterated logarithm.…”

Equivalent conditions of complete $p$-th moment convergence for weighted sums of i. i. d. random variables under sublinear expectations

“…Xu and Cheng [7] studied precise asymptotics in the law of iterated logarithm under sublinear expectations. The interested reader could refer to Xu and Zhang [8,9], Chen [10], Gao and Xu [11], Fang et al [12], Hu et al [13], Hu and Yang [14], Huang and Wu [15], Kuczmaszewska [16], Ma and Wu [17], Wang and Wu [18], Wu and Jiang [19], Yu and Wu [20], Zhang [21], Zhong and Wu [22] and references therein for more limit theorems under sublinear expectations.…”