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

Abstract

We investigate the complete p th moment convergence for weighted sums of independent, identically distributed random variables under sublinear expectations space. Using moment inequality and truncation methods, we prove the equivalent conditions of complete p th moment convergence of weighted sums of independent, identically distributed random variables under sublinear expectations space, which complement the corresponding results obtained in Guo and Shan (2020).

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

“…1 Email: mingzhouxu@whu.edu.cn 2 Email: chengkun0010@126.com equivalent conditions of complete p-th moment convergence of weighted sums of independent, identically distributed random variables under sublinear expectations space, which complement the corresponding results obtained in Guo and Shan [23], also extend results in Xu and Cheng [24] from complete convergence to complete p-th monent convergence. We organized the rest of this paper as follows.…”

“…As in Xu and Cheng [24], we adopt similar notations as in the work by Peng [2] and Chen [10]. Suppose that (Ω, F) is a given measurable space.…”

“…[also cf. Lemma 2.3 in Xu and Cheng [24]]Suppose that {X i , 1 ≤ i ≤ n} is a sequence of independent random variables under sublinear expectation space (Ω,…”

“…Recently Guo and Shan [23] studied equivalent conditions of complete q-th moment convergence for weighted sums of sequences of negatively orthant dependent random variables. Xu and Cheng [24] obtained equivalent conditions of complete convergence for weighted sums of sequences of i. i. d. random variables under sublinear expectations. Motivated by the work of Guo and Shan [23], Xu and Cheng [24], here we try to prove the Supported by Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University (Nos.102/01003002031), Scientific Program of Department of Education of Jiangxi Province of China (Nos.…”

“…Xu and Cheng [24] obtained equivalent conditions of complete convergence for weighted sums of sequences of i. i. d. random variables under sublinear expectations. Motivated by the work of Guo and Shan [23], Xu and Cheng [24], here we try to prove the Supported by Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University (Nos.102/01003002031), Scientific Program of Department of Education of Jiangxi Province of China (Nos. GJJ190732, GJJ180737) and Natural Science Foundation Program of Jiangxi Province 20202BABL211005.…”