Donsker's invariance principle under the sub-linear expectation with an application to Chung's law of the iterated logarithm

TL;DR

This paper establishes a new invariance principle for i.i.d. variables under sub-linear expectation, leading to applications like small deviations and Chung's law of the iterated logarithm.

Contribution

It introduces a novel Donsker's invariance principle under sub-linear expectation, extending classical results to a broader probabilistic framework.

Findings

Proves a new invariance principle under sub-linear expectation.

Derives small deviation results under the new framework.

Establishes Chung's law of the iterated logarithm in this setting.

Abstract

We prove a new Donsker's invariance principle for independent and identically distributed random variables under the sub-linear expectation. As applications, the small deviations and Chung's law of the iterated logarithm are obtained.