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).
Highlights
Peng [1, 2] presented the concept of the sublinear expectation space to study the uncertainty of probability and distribution. e seminal work of Peng [1, 2] encourages people to study limit theorems under sublinear expectations space
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
Motivated by the work of Guo and Shan [23] and Xu and Cheng [24], here we try to prove the equivalent conditions of complete pth 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], extend results in Xu and Cheng [24] from complete convergence to complete pth moment convergence
Summary
Peng [1, 2] presented the concept of the sublinear expectation space to study the uncertainty of probability and distribution. e seminal work of Peng [1, 2] encourages people to study limit theorems under sublinear expectations space. Peng [1, 2] presented the concept of the sublinear expectation space to study the uncertainty of probability and distribution. E seminal work of Peng [1, 2] encourages people to study limit theorems under sublinear expectations space. Motivated by the work of Guo and Shan [23] and Xu and Cheng [24], here we try to prove the equivalent conditions of complete pth 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], extend results in Xu and Cheng [24] from complete convergence to complete pth moment convergence.
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