Open AccessA general form for precise asymptotics for complete convergence under sublinear expectation
Author(s) -
Xue Deng
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022096
Subject(s) - sublinear function , mathematics , sequence (biology) , convergence (economics) , function (biology) , independent and identically distributed random variables , combinatorics , rate of convergence , space (punctuation) , limit (mathematics) , boundary (topology) , random variable , discrete mathematics , mathematical analysis , statistics , computer science , economics , biology , economic growth , computer network , operating system , channel (broadcasting) , genetics , evolutionary biology
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 ] .