Equivalent conditions of complete $p$-th moment convergence for weighted sums of i. i. d. random variables under sublinear expectations

TL;DR

This paper establishes equivalent conditions for complete p-th moment convergence of weighted sums of i.i.d. random variables within sublinear expectation spaces, extending previous results with new moment inequality and truncation techniques.

Contribution

It provides novel necessary and sufficient conditions for convergence under sublinear expectations, complementing earlier work by Guo and Shan (2020).

Findings

Derived new moment inequalities for sublinear expectations

Established equivalence conditions for convergence

Extended classical results to sublinear expectation framework

Abstract

We investigate the complete $p$-th moment convergence for weighted sums of independent, identically distributed random variables under sublinear expectations space. Using moment inequality and truncation methods, we prove the equivalent conditions of complete $p$-th moment convergence of weighted sums of independent, identically distributed random variables under sublinear expectations space, which complement the corresponding results obtained in Guo and Shan (2020).