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

TL;DR

This paper extends classical results on moment convergence of sums of i.i.d. random variables to the setting of sublinear expectations, providing new conditions and applications for weighted sums.

Contribution

It establishes equivalent conditions for complete moment convergence under sublinear expectations, extending classical linear expectation results.

Findings

Derived conditions for maximum partial sums convergence

Extended Baum-Katz type results to sublinear expectation space

Provided new theoretical tools for non-linear expectation analysis

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.