Convergence for sums of i. i. d. random variables under sublinear expectations

Abstract

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.

References in corpus (5)

• Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications
• Exponential inequalities under sub-linear expectations with applications to laws of the iterated logarithm
• Strong laws of large numbers for sub-linear expectations
• Donsker's invariance principle under the sub-linear expectation with an application to Chung's law of the iterated logarithm
• Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations