In probability theory, the convergence of dependent random variables is an extremely crucial concept, Complete moment convergence plays an important role in complete convergence, as it provides a more precise characterization of the convergence rate by incorporating moment conditions. Many scholars have conducted research on classical probability limit theory and achieved significant results. Due to the uncertainty in actual events, limit theory in classical probability spaces is no longer applicable. Therefore, in recent years, the limit theory on nonadditive probabilities or nonlinear expectations is a challenging problem that has attracted many researchers, many scholars have extended their research to sublinear expectation space. In this paper, the weighted sums of Extended Negatively Dependent random variables in the sublinear expectation space are studied. Through making full use of the characteristics of sublinear expectation, some inequalities and local Lipschitz functions, the sufficient conditions for their complete moment convergence are explored. Some conclusions in reference twelve are extended by it from the classical probability spaces to the sublinear expectations space, so some conclusions in the literature are improved.

Yanchun Yi, Shuo Li. Complete Moment Convergence for Weighted Sums of Extended Negatively Dependent Random Variables under Sublinear Expectation. Academic Journal of Mathematical Sciences (2025), Vol. 6, Issue 2: 102-112. https://doi.org/10.25236/AJMS.2025.060214.

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