# Convergence rates in the law of large numbers under sublinear expectations

## TL;DR

This paper investigates how quickly averages of i.i.d. random variables converge under sublinear expectations, establishing strong convergence results in $L^p$ and quasi sure senses.

## Contribution

It introduces new convergence rate results for the law of large numbers within the framework of sublinear expectations, extending classical results.

## Key findings

- Established strong $L^p$-convergence for i.i.d. variables under sublinear expectations.
- Proved strongly quasi sure convergence versions of the law of large numbers.
- Extended classical convergence results to the sublinear expectation setting.

## Abstract

In this note, we study convergence rates in the law of large numbers for independent and identically distributed random variables under sublinear expectations. We obtain a strong $L^p$-convergence version and a strongly quasi sure convergence version of the law of large numbers.