A comparison theorem under sublinear expectations and related limit theorems

TL;DR

This paper develops a comparison theorem for independent and convolutionary random vectors under sublinear expectations, leading to new fundamental limit theorems like the law of large numbers and the central limit theorem in this framework.

Contribution

It introduces a comparison theorem under sublinear expectations and derives key limit theorems for convolutionary random vectors, expanding the theoretical foundation.

Findings

Established a comparison theorem for random vectors under sublinear expectations

Proved law of large numbers, central limit theorem, and law of iterated logarithm in this setting

Demonstrated the equivalence in distribution of partial sums for different vector sequences

Abstract

In this paper, on the sublinear expectation space, we establish a comparison theorem between independent and convolutionary random vectors, which states that the partial sums of those two sequences of random vectors are identically distributed. Under the sublinear framework, through the comparison theorem, several fundamental limit theorems for convolutionary random vectors are obtained, including the law of large numbers, the central limit theorem and the law of iterated logarithm.