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In this paper, we prove the equivalent conditions of complete moment convergence of the maximum for partial weighted sums of independent, identically distributed random variables under sublinear expectations space. As applications, the Baum-Katz type results for the maximum for partial weighted sums of independent, identically distributed random variables are established under sublinear expectations space. The results obtained in the article are the extensions of the equivalent conditions of complete moment convergence of the maximum under classical linear expectation space.
The complete convergence for weighted sums of sequences of independent, identically distributed random variables under sublinear expectations space was studied. By moment inequality and truncation methods, we establish the equivalent conditions of co
Under the sublinear expectation $mathbb{E}[cdot]:=sup_{thetain Theta} E_theta[cdot]$ for a given set of linear expectations ${E_theta: thetain Theta}$, we establish a new law of large numbers and a new central limit theorem with rate of convergence.
This short note provides a new and simple proof of the convergence rate for Pengs law of large numbers under sublinear expectations, which improves the corresponding results in Song [15] and Fang et al. [3].
We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that mean-uncertai
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent components. Bo