A law of the iterated logarithm sublinear expectations

TL;DR

This paper extends the law of the iterated logarithm to capacities within the framework of sub-linear expectations, generalizing classical results to a non-linear setting inspired by Peng's work on IID variables.

Contribution

It introduces a law of the iterated logarithm for capacities under sub-linear expectations, expanding the theoretical understanding of stochastic processes in non-linear probability spaces.

Findings

Established a law of the iterated logarithm for capacities

Extended classical laws to sub-linear expectation frameworks

Provided a natural generalization of Kolmogorov and Hartman-Wintner laws

Abstract

In this paper, motivated by the notion of independent identically distributed (IID) random variables under sub-linear expectations initiated by Peng, we investigate a law of the iterated logarithm for capacities. It turns out that our theorem is a natural extension of the Kolmogorov and the Hartman-Wintner laws of the iterated logarithm.