A general form for precise asymptotics for complete convergence under sublinear expectation

AIMS Mathematics

Xue Ding¹ 

[1] College of Mathematics, Jilin University, Changchun 130012, China;

关键词: complete convergence;    precise asymptotics;    sublinear expectation;   

DOI  :  10.3934/math.2022096

来源: DOAJ

【 摘 要 】

Let $ \{X_n, n\geq 1\} $ be a sequence of independent and identically distributed random variables in a sublinear expectation $ (\Omega, \mathcal H, {\mathbb {\widehat{E}}}) $ with a capacity $ {\mathbb V} $ under $ {\mathbb {\widehat{E}}} $. In this paper, under some suitable conditions, I show that a general form of precise asymptotics for complete convergence holds under sublinear expectation. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in studies of complete convergence. The results extend some precise asymptotics for complete convergence theorems from the traditional probability space to the sublinear expectation space. The results also generalize the known results obtained by Xu and Cheng ^[34].

【 授权许可】

Unknown